Question

Find the roots of $2x^2-5x+3$.

Answer 1

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

Given equation is $2x^2-5x+3$.

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

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

From the given equation we have,

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

Step 2: Determine the roots of the equation

$\therefore$The roots of the equation are,

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

$=\frac{5\pm \sqrt{25-24}}{4}$

$=\frac{5\pm 1}{4}$

$=\frac{6}{4},\frac{4}{4}$

$=\frac{3}{2},1$

Hence, the roots of the given equation are $\frac{3}{2}$ and $1$.