Question

Find the roots of the Equation $x^2-5x+6=0$ using the quadratic formula.

Answer 1

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

Given equation is $x^2-5x+6=0$.

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,

$a=1,b=-5,c=6$

Step 2: Determine the roots of the equation

$\therefore$The roots of the equation are,

$x=\frac{-\left(-5\right)\pm \sqrt{{\left(-5\right)}^2-4\times 1\times 6}}{2\times 1}$

$=\frac{5\pm \sqrt{25-24}}{2}$

$=\frac{5\pm 1}{2}$

$=\frac{6}{2},\frac{4}{2}$

$=3,2$

Hence, the roots of the given equation are $3$ and $2$.