Question

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

Answer 1

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

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

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,

$a=2,b=-3,c=-5$

Step 2: Determine the roots of the equation

$\therefore$The roots of the equation are,

$\begin{array}{l}x=\frac{-(-3)\pm \sqrt{3^2-\left(4\right)\left(2\right)(-5)}}{2\left(2\right)}\end{array}$

$\begin{array}{l}=\frac{3\pm \sqrt{49}}{4}\end{array}$

$\begin{array}{l}=\frac{3\pm 7}{4}\end{array}$

$\begin{array}{l}=\frac{5}{2},-1\end{array}$

Hence, the roots of the equation are $\frac{5}{2}$ and $-1$.