Question

Let $f (x) = px^2 + qx + r$ , where $p, q, r$ are constants and $p \neq 0$ . If $f (5) = -3 f (2)$ and $f (-4) = 0$ , then the other root of $f$ is

• A. 3
• B. -7
• C. -2
• D. 2

Answer 1

Answer: (A)

3

Answer 2

$f(x)=p x^{2}+q x +r$ $f(-4)=0$ $\Rightarrow \, 16 p-4 q +r=0$ ...(i) One root is $x=-4$ and $f(5)=-3 f(2)$ $25 p+5 q +r=-3(4 p+2 q +r)$ $\Rightarrow 37 p+11 q+4 r=0$ ...(ii) E (ii) - E (i), we get $\Rightarrow -27 p+27 q =0$ $\Rightarrow p =0$ Then, equation is $p x^{2}+q x +r=0$ Roots $=-4, \alpha$ Sum of roots $=-4 x+\alpha=-\frac{p}{q}=-1$ So, another root $\alpha=3$.