Find the roots of the following quadratic equation,if they exist,by the method of completing the square: $2x^{2} + x - 4 = 0$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Given equation: $2x^{2} + x - 4 = 0$.
Step $1$: Divide the entire equation by $2$ to make the coefficient of $x^{2}$ equal to $1$:
$x^{2} + \frac{1}{2}x - 2 = 0 \Rightarrow x^{2} + \frac{1}{2}x = 2$.
Step $2$: Add the square of half the coefficient of $x$ to both sides. The coefficient of $x$ is $\frac{1}{2}$,so half of it is $\frac{1}{4}$. Adding $(\frac{1}{4})^{2}$ to both sides:
$x^{2} + 2(x)(\frac{1}{4}) + (\frac{1}{4})^{2} = 2 + (\frac{1}{4})^{2}$.
Step $3$: Write the left side as a perfect square:
$(x + \frac{1}{4})^{2} = 2 + \frac{1}{16} = \frac{32 + 1}{16} = \frac{33}{16}$.
Step $4$: Take the square root of both sides:
$x + \frac{1}{4} = \pm \sqrt{\frac{33}{16}} = \pm \frac{\sqrt{33}}{4}$.
Step $5$: Solve for $x$:
$x = -\frac{1}{4} \pm \frac{\sqrt{33}}{4} = \frac{-1 \pm \sqrt{33}}{4}$.
Thus,the roots are $x = \frac{-1 + \sqrt{33}}{4}$ and $x = \frac{-1 - \sqrt{33}}{4}$.

Explore More

Similar Questions

Find the roots of the quadratic equation $6x^{2}-x-2=0$.

Find the roots of the following quadratic equation by factorisation:
$2x^{2} - x + \frac{1}{8} = 0$

Find the discriminant of the quadratic equation $2x^{2}-4x+3=0$,and hence find the nature of its roots.

Find the roots of the quadratic equation by applying the quadratic formula:
$2 x^{2} + x - 4 = 0$

$A$ pole has to be erected at a point on the boundary of a circular park of diameter $13 \, m$ in such a way that the differences of its distances from two diametrically opposite fixed gates $A$ and $B$ on the boundary is $7 \, m$. Is it possible to do so? If yes,at what distances from the two gates should the pole be erected?

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo