Question

The quadratic polynomial $p ( x )$ has the following properties: $p ( x ) \geq 0$ for all real numbers, $p (1)=$ 0 and $p(2)=2$. Find the value of $p(0)+p(3)$.

Answer 1

as $P (1)=0$
$\text { and } p ( x ) \geq 0 \text { hence let } p ( x )= k ( x -1)^2, k >0 $

$p (2)= k =2 \Rightarrow k =2$
$\therefore p ( x )=2( x -1)^2 \Rightarrow p (0)+ p (3)=10$