Question

The quadratic polynomial $p\left(x\right)$ has the following properties: $p\left(x\right)\ge 0$ for all real numbers, $p\left(1\right)=0$ and $p\left(2\right)=2$. Then the value of $p\left(3\right)$ is

Answer 1

$p\left(x\right)\ge 0$ and $p\left(1\right)=0$
$\Rightarrow p\left(x\right)=k(x-1{)}^2,k>0$
Graph of the quadratic equation,

Given : $p\left(2\right)=2$
$\Rightarrow k=2$
$\therefore p\left(x\right)=2(x-1{)}^2$
Now,
$p\left(3\right)=8$