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

Q. 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

Q. Let $p\left(x\right)=a{x}^2+bx+8$ this quadratic polynomial if the min value of the p(x) i.e $6$ when $x=2$ and find the values of $a$ and $b$

Q. For a quadratic polynomial $p\left(x\right)=a{x}^2+bx+c,\alpha +\beta =2$ and $\alpha \beta =-8$ where $\alpha ,\beta$ are zeroes of $p\left(x\right)$.
$\therefore$ The value of $a,b$ and $c$ is ________ respectively.

Q. Let $P\left(x\right)=x^2+bx+c$ be a quadratic polynomial with real coefficients such that $\underset{0}{\overset{1}{\int }}P\left(x\right)dx=1$ and $P\left(x\right)$ leaves remainder $5$ when it is divided by $(x-2).$ Then the value of $9(b+c)$ is equal to :

Q. Let $p\left(x\right)=a{x}^2+bx+c$ be a quadratic polynomial. It can have at most