Question

The least value of the quadratic polynomial, $f(x)=$ $\left(2p^2+1\right)x^2+2\left(4p^2-1\right)x+4\left(2p^2+1\right)$ for real values of $p$ and $x$ is

Answer 1

Answer: 3

$y=2p^2\left(x^2+4x+4\right)+x^2-2x+1+3$
$y=2p^2(x+2{)}^2+(x-1{)}^2+3$
$p=0,x=1$
$y_{\min }=3$