Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $5x^{2} - 4\sqrt{5}x + 4 = 0$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(B) The given quadratic equation is $5x^{2} - 4\sqrt{5}x + 4 = 0$.
Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = 5$,$b = -4\sqrt{5}$,and $c = 4$.
The discriminant $D$ is given by the formula $D = b^{2} - 4ac$.
Substituting the values,we get $D = (-4\sqrt{5})^{2} - 4(5)(4)$.
$D = (16 \times 5) - 80 = 80 - 80 = 0$.
Since the discriminant $D = 0$,the roots of the quadratic equation are real and equal.

Explore More

Similar Questions

The quadratic equation $2x^{2} - \sqrt{5}x + 1 = 0$ has

If the discriminant $D = 0$,then the roots of the quadratic equation $ax^2 + bx + c = 0$ are ..... .

Solve the following quadratic equation using the method of factorization: $x^{2} + 5x - 66 = 0$.

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $9x^2 + 6x + 4 = 0$.

Which of the following equations has $2$ as a root?

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