(46) Find the condition that one root of the equation \( \left(a x^{2}+b x+c-(a /(1))\right. \) is cube of the other
(a) \( a^{4} c^{4}\left(a^{1}+b^{1}\right)+b=0 \)
(b) \( a^{1} c^{1}\binom{1}{a^{2}+c^{2}}+b=0 \)
(c) \( a b c(a+b)+c=0 \)
(d) \( a^{4} b^{4} c^{-1}(a+b+c)=0 \)
(47) If \( x-a \) is one of the factors of the polynomial \( a x^{2}+b x+c \), then one of the roots of \( a x^{2}+b x+c=0 \) is
(a) -a
(b) b
(c) c
(d) a
(48) If \( x^{4}-500=0 \), then the sum of the roots of the equation is
(a) 500
(b) -500
(c) 0
(d)
\( A=2 B \)
(49) To complete a job A \& B take 4 days together. A alone akes wice as long as B alone to finish the same job. How long would each one alone take to do job?
(a) A 12 -days, B 5-days
(b) A 6 days, B 7-days
(c) A 12-days, B 6-days
(d) A 6-days. B 3-days
(50) If \( \alpha, \beta \) are the roots of the equation \( 5 x^{2}-x-2=0 \), then find the equation with \( 2 \alpha, 2 \beta \)
(a) \( 10 x^{2}-3 x-2=0 \)
(b) \( x^{2}-3 x-2=0 \)
(c) \( x^{2}-3 x-1=0 \)
(d) \( 5 x^{2}-2 x-8=0 \)
\( \frac{3}{2 B}-\frac{1}{4} \)
\( B=\frac{4 x^{2}}{2} \)
(51) If one root of the equation \( (b-c) x^{2}+(c-a) x+(a-b)=0 \) is double of the other then 2,2a
(a) \( 2(a-c)^{2}=9(a-b)(b-c) \)
(b) \( (a-c)^{2}=(a-b)(b-c) \)
(c) \( (a-c)=(a-b)(b-c) \)
(d) \( (a-c)=(a-b)^{2}(b-c)^{2} \)
(52) If the roots of the quadratic equation \( 5 x^{2}-p x+1=0 \) are real and distinct then
(b) \( -2 \sqrt{5}>P>2 \sqrt{5} \)
(a) \( -2<\mathrm{P}<2 \)
(c) \( P<-2 \sqrt{5} \) and \( P>\sqrt{5} \)
(d) \( -2 \sqrt{5}<P<2 \sqrt{5} \)