Question

Find the roots of the quadratic equation by using the quadratic formula the following: $-x^2+7x-10=0$.

Answer 1

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

Given equation is $-x^2+7x-10=0$.

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,

$a=-1,b=7,c=-10$

Step 2: Determine the roots of the equation

$\therefore$The roots of the equation are,

$\begin{array}{l}x=\frac{(-7)\pm \sqrt{(-7{)}^2-(4\left)\right(-1\left)\right(-10)}}{2(-1)}\end{array}$

$\begin{array}{l}=\frac{-7\pm \sqrt{9}}{-2}\end{array}$

$\begin{array}{l}=\frac{-7\pm 3}{2}\end{array}$

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

Hence, the roots of the equation are $5$ and $-2$.