Question

If $\alpha \&\beta$ are zeros of p(x) and $\alpha +\beta =24\&\alpha -\beta =8$, then find quadratic polynomial.

Answer 1

$\alpha +\beta =24$ - - - - (a)
$\alpha -\beta =8$ - - - - (b)
Add (a) and (b) we get,
$\alpha +\beta +\alpha -\beta =24+8$
$2\alpha =32$
$\alpha =16$ - - - - (c)
Substitute the value of $\alpha$ (from (c)) in equation (a)
$16+\beta =24$
$\Rightarrow \beta =8$
$\therefore \alpha =16$ and $\beta =8$
The required quadratic equation is $x^2$ - (sum of zeroes) x + Product of zeroes
$=x^2-(\alpha +\beta )x+\alpha \times \beta$
$=x^2-(16+8)x+(16\times 8)$
$=x^2-24x+128$