Question

Find the roots of the quadratic equations given by applying the quadratic formula.
$2x^2+x-4=0$

Answer 1

Solve for the roots of given equation

Given equation is $2x^2+x-4=0$
Sridhar Acharya formula of quadratic equation $a{x}^2+bx+c=0$ is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
Here $a=2,b=1\&c=-4$,

Substituting this in above formula
$$\begin{gathered} \Rightarrow x=\frac{-1\pm \sqrt{{(-1)}^2-4\times 2\times (-4)}}{2\times 2} \\ \Rightarrow x=\frac{-1\pm \sqrt{1+32}}{2\times 2} \\ \Rightarrow x=\frac{-1\pm \sqrt{33}}{4} \\ \Rightarrow x=\frac{\sqrt{33}-1}{4},\frac{-\sqrt{33}-1}{4} \end{gathered}$$

Hence, the required roots are $\frac{\sqrt{33}-1}{4}$ and $\frac{-\sqrt{33}-1}{4}$