Question

Find the roots of the quadratic equation $3x^2-5x-12=0$ by using the quadratic formula.

Answer 1

Step 1: Estimate the value of $a,b$ and $c$

Given equation is $3x^2-5x-12=0$.

According to the Sridharacharya formula, for a given equation $a{x}^2+bx+c$, the roots of this equation are given by

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

From the given equation we have,

$a=3,b=-5,c=-12$

Step 2: Determine the roots of the equation

$\therefore$The roots of the equation are,

$x=\frac{5\pm \sqrt{(-5{)}^2-(4\left)\right(3\left)\right(-12)}}{2\left(3\right)}$

$=\frac{5\pm \sqrt{25+144}}{6}$

$=\frac{5\pm \sqrt{169}}{6}$

$=\frac{5\pm 13}{6}$

$=3,-\frac{4}{3}$

Hence, the roots of the equation are $3$ and $-\frac{4}{3}$.