Question

If $\alpha$ and $\beta$ are the zeros of the quadratic polynomial such that $\alpha +\beta =24$ and $\alpha -\beta =8$ find a quadratic polynomial having a $\alpha$ and $\beta$ as its zeros.

Answer 1

$\alpha +\beta =24⟶\left(i\right)$

$\alpha -\beta =8⟶\left(ii\right)$

Adding $\left(i\right)$ and $\left(ii\right)$

$\therefore 2\alpha =32$

$\alpha =16$

$\beta =8$

$\therefore$ roots are $16$ and $8$

Sum$=24$

Product=$128$

$\therefore f\left(x\right)=K(x^2-24x+128)$