Question

Find a quadratic polynomial, the sum and product of whose zeroes are $-4$ and $3$ respectively.

Answer 1

Let the quadratic polynomial be $a{x}^2+bx+c$ and its zeroes be $\alpha$ and $\beta$
$\alpha +\beta =-4=-\frac{b}{a}$
$\alpha \beta =3=\frac{c}{a}$
If $a=1$, then $b=4,c=3$
so, one quadratic polynomial will be $x^2+4x+3$