CAT 2008 | Question: 10

Question

Let $f(x) = ax^2 + bx +c$, where $a$, $b$ and $c$ are certain constants and $a \neq 0$. It is known that $f(5) = -3 f(2) $ and that 3 is a root of $f(x)=0$.

What is the other root of $f(x)=0?$

• A. $-7$
• B. $-4$
• C. $2$
• D. $6$
• E. cannot be determined

Answer 1

1)3 is root

So we get 9a+3b+c=0

Acc to second condition f(5)=-3f(2)

25a+5b+c=-3(4a+2b+c)

37a+11b+4c=0

Solving this two eqn we get a=b and c=-12a

ax^2+bx+c=ax^2+ax-12a

                    =a(x^2+x-12)

                     =a(x+4)(x-3)

 So other root is - 4