Question

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

• A. $10$
• B. $9$
• C. $8$
• D. $Noneofthese$

Answer 1

Answer: (A)

$10$

$p\left(1\right)=0$
$p\left(2\right)=2$
$letp\left(x\right)=k{(x-1)}^2$
$p\left(2\right)=2$
$\Rightarrow k{(2-1)}^2=2$
$\Rightarrow k=2$
$p\left(3\right)=2{(3-1)}^2$
$=8$
$p\left(0\right)=2{(0-1)}^2$
$=2$
$Hence$
$p\left(0\right)+p\left(3\right)=8+2=10$