Question

Find a quadratic polynomial whose sum and product of its zeroes is $1,-4$ respectively.

Answer 1

Let zeros be $(\alpha ,\beta )$

$\alpha +\beta =\frac{-b}{a}=1$

$\alpha \beta =\frac{C}{a}=-4$

Polynominal is $a{x}^2+bx+C=0\Rightarrow x^2+\frac{bx}{a}+\frac{C}{a}=0$

$x^2-x-4=0$.