Beginning Algebra

Margaret L. Lial, John Hornsby

Chapter 9

Quadratic Equations - all with Video Answers

Educators

Section 1

Solving Quadratic Equations by the Square Root Property

Problem 1

Match equation in Column I with the correct description of its solution in Column II.
A. No real number solutions
B. Two integer solutions
C. Two irrational solutions
D. Two rational solutions that are not integers

$x^{2}=12$

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Problem 2

Match equation in Column I with the correct description of its solution in Column II.
A. No real number solutions
B. Two integer solutions
C. Two irrational solutions
D. Two rational solutions that are not integers

$x^{2}=-9$

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Problem 3

Match equation in Column I with the correct description of its solution in Column II.
A. No real number solutions
B. Two integer solutions
C. Two irrational solutions
D. Two rational solutions that are not integers

$x^{2}=\frac{25}{36}$

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Problem 4

Match equation in Column I with the correct description of its solution in Column II.
A. No real number solutions
B. Two integer solutions
C. Two irrational solutions
D. Two rational solutions that are not integers

$x^{2}=16$

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Problem 5

Solve each equation by the zero-factor property.
$x^{2}-x-56=0$

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Problem 6

Solve each equation by the zero-factor property.
$x^{2}-2 x-99=0$

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Problem 7

Solve each equation by the zero-factor property.
$x^{2}=121$

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Problem 8

Solve each equation by the zero-factor property.
$x^{2}=144$

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Problem 9

Solve each equation by the zero-factor property.
$3 x^{2}-13 x=3$

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Problem 10

Solve each equation by the zero-factor property.
$5 x^{2}-14 x=3$

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Problem 11

Solve equation by using the square root property. Simplify all radicals.
$x^{2}=81$

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Problem 12

Solve equation by using the square root property. Simplify all radicals.
$z^{2}=169$

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Problem 13

Solve equation by using the square root property. Simplify all radicals.
$x^{2}=14$

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Problem 14

Solve equation by using the square root property. Simplify all radicals.
$m^{2}=22$

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Problem 15

Solve equation by using the square root property. Simplify all radicals.
$t^{2}=48$

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Problem 16

Solve equation by using the square root property. Simplify all radicals.
$x^{2}=54$

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Problem 17

Solve equation by using the square root property. Simplify all radicals.
$x^{2}=-100$

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Problem 18

Solve equation by using the square root property. Simplify all radicals.
$m^{2}=-64$

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Problem 19

Solve equation by using the square root property. Simplify all radicals.
$x^{2}=\frac{25}{4}$

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Problem 20

Solve equation by using the square root property. Simplify all radicals.
$m^{2}=\frac{36}{121}$

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Problem 21

Solve equation by using the square root property. Simplify all radicals.
$x^{2}=2.25$

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Problem 22

Solve equation by using the square root property. Simplify all radicals.
$w^{2}=56.25$

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Problem 23

Solve equation by using the square root property. Simplify all radicals.
$r^{2}-3=0$

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Problem 24

Solve equation by using the square root property. Simplify all radicals.
$x^{2}-13=0$

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Problem 25

Solve equation by using the square root property. Simplify all radicals.
$7 x^{2}=4$

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Problem 26

Solve equation by using the square root property. Simplify all radicals.
$3 p^{2}=10$

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Problem 27

Solve equation by using the square root property. Simplify all radicals.
$3 n^{2}-72=0$

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Problem 28

Solve equation by using the square root property. Simplify all radicals.
$5 z^{2}-200=0$

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Problem 29

Solve equation by using the square root property. Simplify all radicals.
$5 x^{2}+4=8$

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Problem 30

Solve equation by using the square root property. Simplify all radicals.
$4 p^{2}-3=7$

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Problem 31

Solve equation by using the square root property. Simplify all radicals.
$2 t^{2}+7=61$

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Problem 32

Solve equation by using the square root property. Simplify all radicals.
$3 x^{2}+8=80$

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Problem 33

Solve equation by using the square root property. Simplify all radicals.
$-8 x^{2}=-64$

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Problem 34

Solve equation by using the square root property. Simplify all radicals.
$-12 x^{2}=-144$

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Problem 35

When a student was asked to solve $x^{2}=81,$ she wrote $\{9\}$ as her answer. Her teacher did not give her full credit. The student argued that because $9^{2}=81,$ her answer had to be correct. WHAT WENT WRONG? Give the correct solution set.

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Problem 36

Explain the square root property for solving equations, and illustrate with an example.

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Problem 37

Solve equation by using the square root property. Simplify all radicals.
$(x-3)^{2}=25$

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Problem 38

Solve equation by using the square root property. Simplify all radicals.
$(x-7)^{2}=16$

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Problem 39

Solve equation by using the square root property. Simplify all radicals.
$(z+5)^{2}=-13$

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Problem 40

Solve equation by using the square root property. Simplify all radicals.
$(m+2)^{2}=-17$

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Problem 41

Solve equation by using the square root property. Simplify all radicals.
$(x-8)^{2}=27$

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Problem 42

Solve equation by using the square root property. Simplify all radicals.
$(p-5)^{2}=40$

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Problem 43

Solve equation by using the square root property. Simplify all radicals.
$(3 x+2)^{2}=49$

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Problem 44

Solve equation by using the square root property. Simplify all radicals.
$(5 t+3)^{2}=36$

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Problem 45

Solve equation by using the square root property. Simplify all radicals.
$(4 x-3)^{2}=9$

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Problem 46

Solve equation by using the square root property. Simplify all radicals.
$(7 z-5)^{2}=25$

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Problem 47

Solve equation by using the square root property. Simplify all radicals.
$(5-2 x)^{2}=30$

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Problem 48

Solve equation by using the square root property. Simplify all radicals.
$(3-2 x)^{2}=70$

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Problem 49

Solve equation by using the square root property. Simplify all radicals.
$(3 k+1)^{2}=18$

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Problem 50

Solve equation by using the square root property. Simplify all radicals.
$(5 z+6)^{2}=75$

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Problem 51

Solve equation by using the square root property. Simplify all radicals.
$\left(\frac{1}{2} x+5\right)^{2}=12$

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Problem 52

Solve equation by using the square root property. Simplify all radicals.
$\left(\frac{1}{3} m+4\right)^{2}=27$

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Problem 53

Solve equation by using the square root property. Simplify all radicals.
$(4 x-1)^{2}-48=0$

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Problem 54

Solve equation by using the square root property. Simplify all radicals.
$(2 x-5)^{2}-180=0$

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Problem 55

Jeff solved the equation in Exercise 47 and wrote his answer as $\left\{\frac{5+\sqrt{30}}{2}, \frac{5-\sqrt{30}}{2}\right\} .$ Linda solved the same equation and wrote her answer as $\left\{\frac{-5+\sqrt{30}}{-2}, \frac{-5-\sqrt{30}}{-2}\right\} .$ The teacher gave them both full credit. Explain why both students were correct.

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Problem 56

In the solutions $\frac{2 \pm 3 \sqrt{3}}{3}$ found in Example 4 of this section, why is it not valid to $\operatorname{sim}$ plify the answers by dividing out the 3 's in the numerator and denominator?

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Problem 57

Use a calculator with a square root key to solve each equation. Round your answers to the
nearest hundredth.
$(k+2.14)^{2}=5.46$

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Problem 58

Use a calculator with a square root key to solve each equation. Round your answers to the
nearest hundredth.
$(r-3.91)^{2}=9.28$

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Problem 59

Use a calculator with a square root key to solve each equation. Round your answers to the
nearest hundredth.
$(2.11 p+3.42)^{2}=9.58$

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Problem 60

Use a calculator with a square root key to solve each equation. Round your answers to the
nearest hundredth.
$(1.71 m-6.20)^{2}=5.41$

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Problem 61

One expert at marksmanship can hold a silver dollar at forehead level, drop it, draw his gun, and shoot the coin as it passes waist level. The distance traveled by a falling object is given by
$$d=16 t^{2}$$
where $d$ is the distance (in feet) the object falls in $t$ seconds. If the coin falls about $4 \mathrm{ft}$, use the formula to estimate the time that elapses between the dropping of the coin and the shot.

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Problem 62

The illumination produced by a light source depends on the distance from the source. For a particular light source, this relationship can be expressed as
$$I=\frac{4050}{d^{2}}$$
where $I$ is the amount of illumination in foot- candles and $d$ is the distance from the light source (in feet). How far from the source is the illumination equal to 50 footcandles?

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Problem 63

The area $\mathscr{A}$ of a circle with radius $r$ is given by the formula
$$\mathscr{A}=\pi r^{2}$$
If a circle has area $81 \pi$ in. , what is its radius?

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Problem 64

The surface area $S$ of a sphere with radius $r$ is given by the formula
$$S=4 \pi r^{2}$$
If a sphere has surface area $36 \pi \mathrm{ft}^{2}$. what is its radius?

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Problem 65

The amount A that $P$ dollars invested at an annual rate of interest r will grow to in 2 yr is $A=P(1+r)^{2}$.
At what interest rate will $\$ 100$ grow to $\$ 104.04$ in 2 yr?

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Problem 66

The amount A that $P$ dollars invested at an annual rate of interest r will grow to in 2 yr is $A=P(1+r)^{2}$.
At what interest rate will $\$ 500$ grow to $\$ 530.45$ in 2 yr?

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Problem 67

Simplify all radicals, and combine like terms. Express fractions in lowest terms.
$\frac{4}{5}+\sqrt{\frac{48}{25}}$

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Problem 68

Simplify all radicals, and combine like terms. Express fractions in lowest terms.
$\frac{12-\sqrt{27}}{9}$

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Problem 69

Simplify all radicals, and combine like terms. Express fractions in lowest terms.
$\frac{6+\sqrt{24}}{8}$

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Problem 70

Factor each perfect square trinomial.
$z^{2}+4 z+4$

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Problem 71

Factor each perfect square trinomial.
$x^{2}-10 x+25$

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Problem 72

Factor each perfect square trinomial.
$z^{2}+z+\frac{1}{4}$

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