Question

Find the sum and product of the roots of the quadratic equation: $3a^2-10a-5=0$

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 $3a^2-10a-5=0$ is in the form $a{x}^2+bx+c=0$ where $a=3,b=-10$ and $c=-5$.

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

$-\frac{b}{a}=-\frac{(-10)}{3}=\frac{10}{3}$

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

$\frac{c}{a}=\frac{-5}{3}=-\frac{5}{3}$

Hence, sum of the roots is $\frac{10}{3}$ and the product of the roots is $-\frac{5}{3}$.