Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $9x^{2} - 5x + 3 = 0$.
(NONE) Comparing the given equation $9x^{2} - 5x + 3 = 0$ with the standard form $ax^{2} + bx + c = 0$,we get:
$a = 9, b = -5, c = 3$.
Now,calculate the discriminant $D = b^{2} - 4ac$:
$D = (-5)^{2} - 4(9)(3)$
$D = 25 - 108$
$D = -83$.
Since the discriminant $D < 0$,the square root of $D$ is not a real number.
Therefore,the quadratic equation $9x^{2} - 5x + 3 = 0$ has no real roots.
$a = 9, b = -5, c = 3$.
Now,calculate the discriminant $D = b^{2} - 4ac$:
$D = (-5)^{2} - 4(9)(3)$
$D = 25 - 108$
$D = -83$.
Since the discriminant $D < 0$,the square root of $D$ is not a real number.
Therefore,the quadratic equation $9x^{2} - 5x + 3 = 0$ has no real roots.
Explore More
Similar Questions
Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x(x - 5) = 36$.
Medium
View SolutionIf the following quadratic equation has two equal and real roots,then find the value of $k$: $x(4 - kx) = 3 - 2x$.
Medium
View SolutionState whether the quadratic equation $2 x^{2}+x-1=0$ has two distinct real roots. Justify your answer.
Easy
View SolutionFind whether the following equation has real roots. If real roots exist,find them.
$\frac{1}{2x-3} + \frac{1}{x-5} = 1, x \neq \frac{3}{2}, 5$
$\frac{1}{2x-3} + \frac{1}{x-5} = 1, x \neq \frac{3}{2}, 5$
Difficult
View SolutionWhich of the following equations has the sum of its roots as $3$?
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo