Question

Let $P ( x )$ be a quadratic polynomial on $R$ such that $p ( x )$ is negative or zero for all real number. If $p(2)=0$ and $p(3)=-2$, then $p(4)$ is equal to

• A. -3
• B. -4
• C. -8
• D. -16

Answer 1

Answer: (C)

$ \because p ( x )$ is negative or zero for all real numbers and $p (2)=0$
$\therefore p ( x )= k ( x -2)^2, k <0 $
$\because p (3)=-2= k (3-2)^2 \Rightarrow k =-2$
$\therefore p ( x )=-2( x -2)^2 \Rightarrow p (4)=-2 \times 4=-8 .$