Question

Find the sum and product of the roots of the quadratic equation: $8m^2-m=2$

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 $8m^2-m=2$ can be rewritten as $8m^2-m-2=0$ is in the form $a{x}^2+bx+c=0$ where $a=8,b=-1$ and $c=-2$.

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

$-\frac{b}{a}=-\frac{(-1)}{8}=\frac{1}{8}$

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

$\frac{c}{a}=\frac{-2}{8}=-\frac{1}{4}$

Hence, sum of the roots is $\frac{1}{8}$ and the product of the roots is $-\frac{1}{4}$.