Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $3x^{2} - 18x + 27 = 0$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) The given quadratic equation is $3x^{2} - 18x + 27 = 0$.
Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = 3$,$b = -18$,and $c = 27$.
The discriminant $D$ is given by the formula $D = b^{2} - 4ac$.
Substituting the values: $D = (-18)^{2} - 4(3)(27)$.
$D = 324 - 324 = 0$.
Since the discriminant $D = 0$,the roots of the quadratic equation are real,rational,and equal.

Explore More

Similar Questions

If one root of a quadratic equation $ax^2 + bx + c = 0$ is $\frac{-b + \sqrt{D}}{2a}$,then the other root is $\ldots \ldots \ldots \ldots$.

While selling a pen for Rs. $24$, the loss percentage is equal to its cost price in rupees. Find the cost price of the pen.

Difficult
View Solution

Obtain the roots of the following quadratic equation by using the general formula for the solution: $3x^{2} - 2x + 2 = 0$

If the roots of the quadratic equation $5x(2x - 3) - 4 = 0$ exist,find them using the method of completing the square.

If one root of $x^{2}-5x+6=0$ is also the root of $x^{2}+3x+c=0$,then $c = \ldots$

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