Question

If $\alpha ,\beta$ are the roots of the quadratic equation $x^2-8x+p=0$, find the value of p if ${\alpha }^2+{\beta }^2=40$.

• A. 8
• B. 10
• C. 12
• D. 6

Answer 1

The correct option is C 12

$\because \alpha ,\beta$ are the roots of the quadratic equation
$x^2-8x+p=0$
$a=1,b=-8,c=p$
$\therefore \alpha +\beta =-\frac{b}{a}=\frac{8}{1}=8$
and $\alpha .\beta =\frac{c}{d}=\frac{p}{1}=p$
Now, ${(\alpha +\beta )}^2={\alpha }^2+{\beta }^2+2\alpha .\beta$
$\Rightarrow {\left(8\right)}^2=40+2p$
$\Rightarrow 64=40+2p$
$\Rightarrow 2p=64-40=24$
$\therefore p=\frac{24}{2}=12$