Question

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.

• A. $a,-2a,-8a$
• B. $a,2a,8a$
• C. $b,b,4b$
• D. $2b,b,4b$

Answer 1

The correct option is A $a,-2a,-8a$

If

$p\left(x\right)=a{x}^2+bx+c$ where $a\ne 0$ is a quadratic polynomial

And $\alpha ,\beta$ are the zeroes of the polynomial $p\left(x\right)$

Then,

$\alpha +\beta =\frac{-b}{a}$ and $\alpha \times \beta =\frac{c}{a}$

Given that

$\alpha +\beta =2=\frac{-b}{a}$

$\alpha \times \beta =-8=\frac{c}{a}$

$\Rightarrow b=-2a,c=-8a$