Chapter Questions
The roots of the equation $3 x^{2}-2 x+3=0$ are(1) real and distinct.(2) real and equal.(3) imaginary.(4) irrational and distinct.
Find the sum and the product of the roots of the equation $\sqrt{3} \mathrm{x}^{2}+27 \mathrm{x}+5 \sqrt{3}=0$.(1) $-9 \sqrt{3}, 5$(2) $9 \sqrt{3}, 5$(3) $6 \sqrt{3},-5$(4) $6 \sqrt{3}, 5$
If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-12 x+32=0$, then find the value of $\frac{\alpha^{2}+\beta^{2}}{\alpha+\beta}$.(1) $\frac{-8}{3}$(2) $\frac{8}{3}$(3) $\frac{-20}{3}$(4) $\frac{20}{3}$
Find the maximum or minimum value of the quadratic expression, $\mathrm{x}^{2}-3 \mathrm{x}+5$ whichever exists.(1) The minimum value is $\frac{9}{10}$.(2) The minimum value is $\frac{11}{4}$.(3) The maximum value is $\frac{9}{10}$.(4) The maximum value is $\frac{11}{4}$.
Find the values of $x$ which satisfy the equation $\sqrt{3 x+7}-\sqrt{2 x+3}=1$.(1) $2,-2$(2) 4,3(3) $5,-1$(4) $3,-1$
If one of the roots of a quadratic equation having rational coefficients is $\sqrt{7}-4$, then the quadratic equation is(1) $x^{2}-2 \sqrt{7} x-9=0 .$(2) $\mathrm{x}^{2}-8 \mathrm{x}+9=0$.(3) $\mathrm{x}^{2}+8 \mathrm{x}+9=0 .$(4) $\mathrm{x}^{2}-2 \sqrt{7} \mathrm{x}+9=0 .$
If the quadratic equation $\mathrm{px}^{2}+\mathrm{qx}-\mathrm{r}=0(\mathrm{p} \neq 0)$ is to be solved by the graphical method, then which of the following graphs have to be drawn?(1) $\mathrm{y}=\mathrm{x}^{2}, \mathrm{y}=\mathrm{r}-\mathrm{q} \mathrm{x}$(2) $\mathrm{y}=\mathrm{px}^{2}, \mathrm{y}=\mathrm{qx}-\mathrm{r}$(3) $\mathrm{y}=\mathrm{x}^{2}, \mathrm{qx}+\mathrm{py}-\mathrm{r}=0$(4) $\mathrm{y}=\mathrm{x}^{2}, \mathrm{qx}-\mathrm{py}=\mathrm{r}$
If the roots of the equation $a x^{2}+b x+c=0$ are $\alpha$ and $\beta$, then the quadratic equation whose roots are $-\alpha$ and $-\beta$ is(1) $a x^{2}-b x-c=0$.(2) $a x^{2}-b x+c=0$(3) $a x^{2}+b x-c=0 .$(4) $a x^{2}-b x+2 c=0$
Find the sum and the product of the roots of the quadratic equation $-x^{2}-\frac{25}{3} x+25=0$(1) $\frac{25}{3}, 25$(2) $\frac{-25}{3}, 25$(3) $\frac{25}{3},-25$(4) $\frac{-25}{3},-25$
For what value of $\mathrm{k}$ is one root of the quadratic equation $9 \mathrm{x}^{2}-18 \mathrm{x}+\mathrm{k}=0$ double the other?(1) 36(2) 9.(3) 12(4) 8
The sum of a number and its square is greater than 6 , then the number belongs to(1) $(-\infty, 2) \cup(3, \infty)$(2) $(-\infty,-3) \cup(2, \infty)$(3) $(2,3)$(4) $[2,3]$
For which of the following intervals of $x$ is $x^{2}>\frac{1}{x^{2}}$ ?(1) $(-\infty,-1) \cup(1, \infty)$(2) $(-\infty,-1) \cup(1, \infty)$(3) $(-1,1)$(4) $[-1,1]$
If $x$ and $y$ are two successive multiples of 2 and their product is less than 35 , then find the range of $x$.(1) $\{2,4,0\}$(2) $\{-6,-4,-2,2,4,6\}$(3) $\{-6,-4,-2,0,2,4\}$(4) $\{-6,-4,-2,0,2,4,6\}$
If $x^{2}<n$, and $n \in(-\infty, 0)$, then $x$(1) is any real number.(2) is only positive number.(3) has no value.(4) is any negative number.
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $a x^{2}+b x+c$ such that $x$ does not lie between $\alpha$ and $\beta$, then(1) $a>0$ and $a x^{2}+b x+c<0$(2) $a x^{2}+b x+c \leq 0$ and $a<0$(3) $\mathrm{a}>0$ and $\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}>0$(4) both (2) and (3).
The condition for the sum and the product of the roots of the quadratic equation $a x^{2}-b x+c=0$ to be equal, is(1) $\mathrm{b}+\mathrm{c}=0$.(2) $\mathrm{b}-\mathrm{c}=0$.(3) $a+c=0$.(4) $a+b+c=0$.
The quadratic equation having rational coefficients and one of the roots as $4+\sqrt{15}$ is(1) $\mathrm{x}^{2}-8 \mathrm{x}+1=0$.(2) $\mathrm{x}^{2}+\mathrm{x}-8=0 .$(3) $\mathrm{x}^{2}-\mathrm{x}+8=0$.(4) $\mathrm{x}^{2}+8 \mathrm{x}+8=0$.
If $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $a x^{2}+b x+c$ and $x$ lies between $\alpha$ and $\beta$, then which of the following is true?(1) If $\mathrm{a}<0$ then $\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}>0 .$(2) If $\mathrm{a}>0$ then $\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}<0 .$(3) If $\mathrm{a}>0$ then $\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}>0$.(4) Both (1) and (2).
Find the nature of the roots of the equation $4 \mathrm{x}^{2}-2 \mathrm{x}-1=0$.(1) real and equal(2) rational and unequal(3) irrational and unequal(4) imaginary
The solution of the inequation, $15 x^{2}-31 x+14<0$ is given by(1) $\mathrm{x} \in\left(\frac{7}{5}, \infty\right)$(2) $\frac{2}{3}<x<\frac{7}{5}$(3) $\mathrm{x} \in\left(\frac{7}{5}, \infty\right)$(4) $\mathrm{x} \in \mathrm{R}$
If $m x^{2}<n x$ such that $m$ and $n$ have opposite signs, then which of the following can be true?(1) $\mathrm{x} \in\left(\frac{\mathrm{n}}{\mathrm{m}}, \infty\right)$(2) $\mathrm{x} \in\left(-\infty, \frac{\mathrm{n}}{\mathrm{m}}\right)$(3) $\mathrm{x} \in\left(\frac{\mathrm{n}}{\mathrm{m}}, 0\right)$(4) None of these
Find the range of values of $x$ which satisfy the inequation, $(x+1)^{2}+(x-1)^{2}<6$.(1) $(-\sqrt{2}, \sqrt{2})$(2) $(-1,1)$(3) $(-\infty,-2) \cup(2, \infty)$(4) $(-\infty,-1) \cup(1, \infty)$
If the sum of the squares of three consecutive odd natural numbers is 155, then their product will be equal to(1) 99(2) 105(3) 693(4) 315
If $\mathrm{x}^{2}>0$, then find the range of the values that $\mathrm{x}$ can take.(1) $\mathrm{x}=0$(2) $\mathrm{x} \in \mathrm{R}$(3) $\mathrm{x} \in(0, \infty)$(4) $\mathrm{x} \in \mathrm{R}-\{0\}$
Find the range of the values of $x$ which satisfy the inequation, $x^{2}-7 x+3<2 x+25$.(1) $(-2,11)$(2) $(2,11)$(3) $(-\infty,-1) \cup(2,11)$(4) $(-8,-2) \cup[11, \infty)$
If $\mathrm{A}$ and $\mathrm{B}$ are the roots of the quadratic equation $\mathrm{x}^{2}-12 \mathrm{x}+27=0$, then $\mathrm{A}^{3}+\mathrm{B}^{3}$ is(1) 27(2) 729(3) 756(4) 64
By drawing which of the following graphs can the quadratic equation $4 x^{2}+6 x-5=0$ be solved by graphical method?(1) $y=x^{2}, 3 x-2 y-5=0$(2) $y=4 x^{2}, 6 x-2 y-5=0$(3) $y=x^{2}, 6 x-y-5=0$(4) $\mathrm{y}=2 \mathrm{x}^{2}, 6 \mathrm{x}+2 \mathrm{y}-5=0$
If the quadratic equation $\left(a^{2}-b^{2}\right) x^{2}+\left(b^{2}-c^{2}\right) x+\left(c^{2}-a^{2}\right)=0$ has equal roots, then which of the following is true?(1) $\mathrm{b}^{2}+\mathrm{c}^{2}=\mathrm{a}^{2}$(2) $\mathrm{b}^{2}+\mathrm{c}^{2}=2 \mathrm{a}^{2}$(3) $b^{2}-c^{2}=2 a^{2}$(4) $a^{2}=b^{2}+2 c^{2}$
Which of the following are the roots of the equation $|x|^{2}+|x|-6=0 ?$(a) 2(b) $-2$(c) 3(d) $-3$(1) Both (a) and (b).(2) Both (c) and (d).(3) (a), (b), (c) and (d).(4) None of the above.
What are the values of $x$ which satisfy the equation, $\sqrt{5 x-6}+\frac{1}{\sqrt{5 x-6}}=\frac{10}{3} ?$(1) 3(2) $4, \frac{11}{9}$(3) $\frac{11}{9}$(4) $3, \frac{11}{9}$
If the roots of the equation $3 \mathrm{ax}^{2}+2 \mathrm{bx}+\mathrm{c}=0$ are in the ratio $2: 3$, then(1) $8 a c=25 b$.(2) $8 a c=9 b^{2}$.(3) $8 \mathrm{~b}^{2}=9 \mathrm{ac}$(4) $8 \mathrm{~b}^{2}=25 \mathrm{ac}$.
If $3.2^{2 x+1}-5.2^{x+2}+16=0$ and $x$ is an integer, find the value of $x$.(1) 1(2) 2(3) 3(4) 4
If $(x+1)(x+3)(x+5)(x+7)=5760$, find the real values of $x$(1) $5,-13$(2) $-5,13$(3) $-5,-13$(4) 5,13
Find the roots of the equation $\ell^{2}\left(\mathrm{~m}^{2}-\mathrm{n}^{2}\right) \mathrm{x}^{2}+\mathrm{m}^{2}\left(\mathrm{n}^{2}-\ell^{2}\right) \mathrm{x}+\mathrm{n}^{2}\left(\ell^{2}-\mathrm{m}^{2}\right)=0$(1) $1, \frac{\mathrm{n}^{2}\left(\ell^{2}-\mathrm{m}^{2}\right)}{\ell^{2}\left(\mathrm{~m}^{2}-\mathrm{n}^{2}\right)}$(2) $1, \frac{-\mathrm{m}^{2}\left(\ell^{2}-\mathrm{n}^{2}\right)}{\ell^{2}\left(\mathrm{~m}^{2}-\mathrm{n}^{2}\right)}$(3) $1, \frac{\mathrm{n}^{2}\left(\ell^{2}+\mathrm{m}^{2}\right)}{\ell^{2}\left(\mathrm{~m}^{2}-\mathrm{n}^{2}\right)}$(4) $1, \frac{-m^{2}\left(\ell^{2}+n^{2}\right)}{\ell^{2}\left(m^{2}-n^{2}\right)}$
In writing a quadratic equation of the form $\mathrm{x}^{2}+\mathrm{bx}+\mathrm{c}=0$, a student writes the coefficient of $\mathrm{x}$ incorrectly and finds the roots as $-6$ and 7 . Another student makes a mistake in writing the constant term and finds the roots as 4 and 11 . Find the correct quadratic equation.(1) $x^{2}+15 x-42=0$(2) $\mathrm{x}^{2}+\mathrm{x}+44=0$(3) $x^{2}-15 x-42=0$(3) $\mathrm{x}^{2}-\mathrm{x}+44=0$
Comment on the sign of the quadratic expression $x^{2}-5 x+6$ for all $x \in R$.(1) $x^{2}-5 x+6 \geq 0$ when $2 \leq x \leq 3$ and(2) $x^{2}-5 x+6 \leq 0$ when $2 \leq x \leq 3$ and $x^{2}-5 x+6<0$ when $x<2$ or $x>3 \quad x^{2}-5 x+6>0$ when $x<2$ or $x>3$(3) $\mathrm{x}^{2}-5 \mathrm{x}+6 \leq 0$ when $-1 \leq \mathrm{x} \leq 6$ and(4) $x^{2}-5 x+6 \geq 0$ when $-1 \leq x \leq 6$ and $\mathrm{x}^{2}-5 \mathrm{x}+6>0$ when $\mathrm{x}<-1$ or $\mathrm{x}>6 \quad \mathrm{x}^{2}-5 \mathrm{x}+6<0$ when $\mathrm{x}<-1$ or $\mathrm{x}>6$
If $a-b, b-c$ are the roots of $a x^{2}+b x+c=0$, then find the value of $\frac{(a-b)(b-c)}{c-a}$.(1) $\frac{\mathrm{b}}{\mathrm{c}}$(2) $\frac{\mathrm{c}}{\mathrm{b}}$(3) $\frac{a b}{c}$(4) $\frac{\mathrm{bc}}{\mathrm{a}}$
The values of $x$ for which $\frac{x+3}{x^{2}-3 x-54} \geq 0$ are(1) $(-6,-3) \cup(9, \infty)$(2) $[-6,-3] \cup[9, \infty]$(3) $(-6,-3) \cup(9, \infty)$(4) $(-6, \infty)$
In a right triangle, the base is 3 units more than the height. If the area of the triangle is less than 20 sq.units, then the possible values of the base lie in the region(1) $(4,6)$(2) $(3,8)$(3) $(6,8)$(4) $(5,8)$
A man bought 50 dozen fruits consisting of apples and bananas. An apple is cheaper than a banana. The number of dozens of apples he bought is equal to the cost per dozen of bananas in rupees and vice versa. If he had spent a total amount of $\mathrm{Rs} 1050$, find the number of dozens of apples and bananas he bought respectively.(1) 12 and 38(2) 14 and 36(3) 15 and 35(4) 18 and 32
The values of $x$ for which $-2 x-4 \leq(x+2)^{2} \leq-2 x-1$ is satisfied are(1) $[-5,-1]$.(2) $[-5,0]$(3) $[-5,-4] \cup[-2,-1]$.(4) $[-5,-4] \cup[-2,-1] .$
If $\frac{x^{2}+x-12}{x^{2}-3 x+2}<0$, then $x$ lies in(1) $(-4,3)$(2) $(-4,2)$(3) $[-4,1] \cup[2,3]$(4) $(-4,1) \cup(2,3)$
For all real values of $x, \frac{x^{2}-\left(\frac{x}{2}\right)+1}{x^{2}+1}-\frac{5}{4}$ is(1) equal to 1(2) non-negative(3) greater than $\frac{1}{4}$(4) non-positive
If $x^{2}-4 x+3>0$ and $x^{2}-6 x+8<0$, then(1) $x>3$(2) $x<4$(3) $3<x<4$(4) $1<\mathrm{x}<2$
Find the product of the roots of $\mathrm{x}^{2}+8 \mathrm{x}-16=0$.(1) 8(2) $-8$(3) 16(4) $-16$
For what value of $\mathrm{x}:-3 \mathrm{x}^{2}+5 \mathrm{x}-12$ has maximum value?(1) $-\frac{5}{3}$(2) $\frac{5}{6}$(3) $-\frac{5}{6}$(4) $\frac{5}{3}$
If the roots of the equation $2 \mathrm{x}^{2}+7 \mathrm{x}+4=0$ are in the ratio $\mathrm{p}: \mathrm{q}$, then find the value of $\sqrt{\frac{\mathrm{p}}{\mathrm{q}}}+\sqrt{\frac{\mathrm{q}}{\mathrm{p}}}$(1) $\pm \frac{7}{\sqrt{2}}$(2) $\pm 7 \sqrt{2}$(3) $\pm \frac{7 \sqrt{2}}{16}$(4) $\pm \frac{7 \sqrt{2}}{4}$
In a forest, a certain number of apes equal to the square of one-eighth of the total number of their group are playing and having great fun. The rest of them are twelve in number and are on an adjoining hill. The echo of their shrieks from the hills frightens them. They come and join the apes in the forest and play with enthusiasm. What is the total number of apes in the forest?(1) 16(2) 48(3) 16 or 48(4) 64
If the roots of the quadratic equation $x^{2}-2 \mathrm{kx}+2 \mathrm{k}^{2}-4=0$ are real, then the range of the values of $\mathrm{k}$ is(1) $[-2,2]$(2) $[-\infty,-2] \cup[2, \infty]$(3) $[0,2]$(4) None of the above
Find the values of $x$ for which the expression $x^{2}-\left(\log _{5} 2+\log _{2} 5\right) x+1$ is always positive.(1) $x>\log _{2} 5$ or $x<\log _{5} 2$(2) $\log _{5} 2<x<\log _{2} 5$(3) $-\log _{5} 2<x<\log _{2} 5$(4) $x<-\log _{5} 2$ or $x>\log _{2} 5$
Find the values of $x$ which satisfy the quadratic inequation $|x|^{2}-2|x|-8 \leq 0$.(1) $[-4,4]$(2) $[0,4]$(3) $[-4,0]$(4) $[-4,2]$
The roots of the equation $x^{2}-p x+q=0$ are consecutive integers. Find the discriminant of the equation.(1) 1(2) 2(3) 3(4) 4
Rohan ond Sohan were attempting to solve the quadratic equation, $\mathrm{x}^{2}-\mathrm{ax}+\mathrm{b}=0 .$ Rohan copied the coefficient of $x$ wrongly and obtained the roots as 4 and $12 .$ Sohan copied the constant term wrongly and obtained the roots as $-19$ and 3 . Find the correct roots.(1) $-2$ and $-24$(2) 2 and 24(3) 4 and 12(4) $-4$ and $-12$
If $(x+2)(x+4)(x+6)(x+8)=945$ and $x$ is an integer, then find $x$.(1) $-1$ or $-11$(2) 1 or $-11$(3) $-1$ or 11(4) $-1$ or $-11$
The difference of the roots of $2 y^{2}-k y+16=0$ is $\frac{1}{3}$. Find $k$.$(1) \pm \frac{32}{3}$(2) $\pm \frac{34}{3}$(3) $\pm \frac{38}{3}$(4) $\pm \frac{40}{3}$
Find the condition to be satisfied by the coefficients of the equation $\mathrm{px}^{2}+\mathrm{qx}+\mathrm{r}=0$, so that the roots are in the ratio $3: 4$.(1) $12 \mathrm{q}^{2}=49 \mathrm{pr}$(2) $12 \mathrm{q}^{2}=-49 \mathrm{pr}$(3) $49 \mathrm{q}^{2}=12 \mathrm{pr}$(4) $49 \mathrm{q}^{2}=-12 \mathrm{pr}$
If the roots of the equation $3 \mathrm{x}^{2}+9 \mathrm{x}+2=0$ are in the ratio $\mathrm{m}: \mathrm{n}$, then find $\sqrt{\frac{\mathrm{m}}{\mathrm{n}}}+\sqrt{\frac{\mathrm{n}}{\mathrm{m}}}$.(1) $\frac{-3 \sqrt{3}}{\sqrt{2}}$(2) $\frac{3 \sqrt{2}}{2}$(3) $\frac{3 \sqrt{3}}{\sqrt{2}}$(4) $\frac{-3 \sqrt{3}}{2}$
If $\left(\mathrm{p}^{2}-\mathrm{q}^{2}\right) \mathrm{x}^{2}+\left(\mathrm{q}^{2}-\mathrm{r}^{2}\right) \mathrm{x}+\mathrm{r}^{2}-\mathrm{p}^{2}=0$ and $\left(\mathrm{p}^{2}-\mathrm{q}^{2}\right) \mathrm{y}^{2}+\left(\mathrm{r}^{2}-\mathrm{p}^{2}\right) \mathrm{y}+\mathrm{q}^{2}-\mathrm{r}^{2}=0$ have a common rootfor all real values of $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$, then find the common root.(1) $-1$(2) 1(3) 2(4) $-2$
Which of the following are the roots of $|\mathrm{y}|^{2}-|\mathrm{y}|-12=0$ ?(a) 4(b) $-4$(c) 3(d) $-3$(1) Both (a) and (b)(2) Both (c) and (b)(3) (a), (b), (c) and (d)(4) None of the above
Find the value of $\sqrt{30+\sqrt{30+\sqrt{30+\ldots \infty}}}$.(1) 6(2) $-5$(3) Either (1) or (2)(4) Neither (1) nor (2)
If $y^{2}+6 y-3 m=0$ and $y^{2}-3 y+m=0$ have a common root, then find the possible values of $m$.(1) $0,-\frac{27}{16}$(2) $0,-\frac{81}{16}$(3) $0, \frac{81}{16}$(4) $0, \frac{27}{16}$
The students of a class contributed for a programme. Each student contributed the same amount. Had there been 15 more students in the class and each student had contributed Rs 40 less, the total amount contributed would have increased from Rs 3000 to Rs 3200 . Find the strength of the class.(1) 25(2) 15(3) 10(4) None of these
The graphs of $\mathrm{y}=2 \mathrm{x}^{2}$ and $\mathrm{y}=\mathrm{ax}+\mathrm{b}$ intersect at two points $(2,8)$ and $(6,72) .$ Find the quadratic equation in $x$ whose roots are $a+2$ and $\frac{b}{4}-1$(1) $\mathrm{x}^{2}+11 \mathrm{x}-126=0$(2) $x^{2}-11 x+126=0$(3) $\mathrm{x}^{2}+11 \mathrm{x}+126=0$(4) $x^{2}-11 x-126=0$
The equation $9 \mathrm{y}^{2}(\mathrm{~m}+3)+6(\mathrm{~m}-3) \mathrm{y}+(\mathrm{m}+3)=0$, where $\mathrm{m}$ is real, has real roots. Which of the following is true?(1) $\mathrm{m}=0$(2) $\mathrm{m} \leq 0$(3) Either (1) or (2)(4) Neither(1) nor (2)
Find the values of $\mathrm{y}$ which satisfy the quadratic inequalities below $\mathrm{y}^{2}+5 \mathrm{y}+4 \leq 0$ and $\mathrm{y}^{2}-2 \mathrm{y}-$ $15 \geq 0$(1) $-1 \leq \mathrm{y} \leq 5$(2) $-4 \leq \mathrm{y} \leq-3$(3) Either (1) or (2)(4) Neither (1) nor (2)
If $\frac{y^{2}+y-6}{y^{2}+y-2}<0$, then which of the following is true?(1) $1<\mathrm{y}<2$(2) $-3<\mathrm{y}<-2$(3) Either (1) or (2)(4) Neither (1) nor (2)
The product of two consecutive even numbers exceeds twice their sum by more than $20 .$ Which of the following is the range of values that the smaller of the numbers can take?(1) $x>4$ or $x<-6$(2) $-6<x<4$(3) $\mathrm{x}>6$ or $\mathrm{x}<-4$(4) $-4<x<6$
Which of the following statements about the sign of the quadratic expression $\mathrm{E}=\mathrm{y}^{2}-12 \mathrm{y}+20$ is true?(1) $\mathrm{E} \leq 0$ when $2 \leq \mathrm{y} \leq 10$ and $\mathrm{E}>0$ when $\mathrm{y}<2$ or $\mathrm{y}>10$(2) $\mathrm{E} \geq 0$ when $2 \leq \mathrm{y} \leq 10$ and $\mathrm{E}<0$ when $\mathrm{y}<2$ or $\mathrm{y}>10$(3) $\mathrm{E} \leq 0$ when $-10 \leq \mathrm{y} \leq-2$ and $\mathrm{E}>0$ when $\mathrm{y}<-10$ or $\mathrm{y}>-2$(4) $\mathrm{E} \geq-2$ and $\mathrm{E}<0$ when $\mathrm{y}<-10$ or $\mathrm{y}>-2$
If $|\mathrm{y}|^{2}-4|\mathrm{y}|-60 \leq 0$, then which of the following is the range of $\mathrm{y}$ ?(1) $[-6,6]$(2) $[0,6]$(3) $[0,10]$(4) $[-10,10]$