Question

Find the sum and product of the roots of the quadratic equation:$x^2+\left(ab\right)x+(a+b)=0$

Answer 1

We know that for a quadratic equation $a{x}^2+bx+c=0$, the sum of the roots is $-\frac{b}{a}$ and the product of the roots is $\frac{c}{a}$.

Here, the given quadratic equation $x^2+\left(ab\right)x+(a+b)=0$ is in the form $a{x}^2+bx+c=0$ where $a=1,b=ab$ and $c=(a+b)$.

The sum of the roots is $-\frac{b}{a}$ that is:

$-\frac{b}{a}=-\frac{ab}{1}=-ab$

The product of the roots is $\frac{c}{a}$ that is:

$\frac{c}{a}=\frac{a+b}{1}=a+b$

Hence, sum of the roots is $(-ab)$ and the product of the roots is $(a+b)$.