Question

Find a quadratic equation whose sum & product of zeros are -4 and -1 respectively .

Answer 1

For $a{x}^2+bx+c=0$

Sum of roots$=\frac{-b}{a}$, Product of roots$=\frac{c}{a}$

$-4-1=-\frac{b}{a}$ $(-4)(-1)=\frac{c}{a}$

$\frac{b}{a}=5$ $4=\frac{c}{a}$

$a{x}^2+bx+c=0$

$\Rightarrow x^2+\frac{b}{a}x+\frac{c}{a}=0$

$\Rightarrow x^2+5x+4=0$.