Question

Let $P\left(x\right)=a{x}^2+bx+8$ is a quadratic polynomial. If the minimum value of $P\left(x\right)$ is $6$ at $x=2,$ then

• A. $a=\frac{1}{2}$
• B. $b=-\frac{1}{2}$
• C. $a=2$
• D. $b=-2$

Answer 1

Answer: (A), (D)

The correct options are
A $a=\frac{1}{2}$
D $b=-2$

$-\frac{b}{2a}=2$
$4a=-b\dots \left(1\right)$
$P\left(2\right)=4a+2b+8=6$
$4a+2b=-2\dots \left(2\right)$

Using $\left(1\right)$ and $\left(2\right)$
$b=-2,a=\frac{1}{2}$