Question

Find the sum and product of the roots of the quadratic equation: $6k^2-3=0$

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 $6k^2-3=0$ is in the form $a{x}^2+bx+c=0$ where $a=6,b=0$ and $c=-3$.

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

$-\frac{b}{a}=-\frac{0}{6}=0$

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

$\frac{c}{a}=\frac{-3}{6}=-\frac{1}{2}$

Hence, sum of the roots is $0$ and the product of the roots is $-\frac{1}{2}$.