Question

If $\alpha ,\beta$ are the roots of a quadratic equation such that $\alpha +\beta =24$ and $\alpha -\beta =8$, the quadratic equation is

• A. $x^2-24x+128=0$
• B. $x^2-8x+16=0$
• C. $x^2-24x+12=0$
• D. $Noneoftheabove$

Answer 1

The correct option is A $x^2-24x+128=0$

$\because \alpha +\beta =24$......(i)
and $\alpha -\beta =\mathrm{8........}\left(ii\right)$
Adding equation (i) and (ii), we get
$2\alpha =32\Rightarrow \alpha =16$
Subtracting equation(ii)- from (i), we get
$2\beta =16\Rightarrow \beta =8$
$\therefore$ Product of the roots i.e.
$\alpha .\beta =16\times 8\Rightarrow 128$
We know that the quadratic equation whose roots are $\alpha$ and $\beta$ is
$x^2-(\alpha +\beta )x+\alpha .\beta =0$
$\Rightarrow x^2-24x+128=0$
which is the required quadratic equation