Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2}+5x+5=0$
(N/A) Comparing the given equation $x^{2}+5x+5=0$ with the standard quadratic form $ax^{2}+bx+c=0$,we get:
$a=1, b=5, c=5$
The discriminant $D$ is given by the formula $D = b^{2}-4ac$.
Substituting the values:
$D = (5)^{2} - 4(1)(5)$
$D = 25 - 20$
$D = 5$
Since $D > 0$,the quadratic equation has two distinct real roots. Furthermore,since $5$ is not a perfect square,the roots are irrational.
$a=1, b=5, c=5$
The discriminant $D$ is given by the formula $D = b^{2}-4ac$.
Substituting the values:
$D = (5)^{2} - 4(1)(5)$
$D = 25 - 20$
$D = 5$
Since $D > 0$,the quadratic equation has two distinct real roots. Furthermore,since $5$ is not a perfect square,the roots are irrational.
Explore More
Similar Questions
If the roots of the following quadratic equation exist,find them by the method of completing the square: $\frac{2}{x^{2}}-\frac{1}{x}=6$.
Medium
View SolutionExamine whether the following equation is quadratic or not: $\sqrt{2} x^{2}-5 \sqrt{3} x+6=0$
Easy
View SolutionFind the roots of the following quadratic equation by using the quadratic formula,if they exist: $2 y^{2}+5 y-3=0$.
Medium
View SolutionState whether the quadratic equation $(x+1)(x-2)+x=0$ has two distinct real roots. Justify your answer.
Medium
View SolutionComparing the quadratic equation $x(2x - 1) - 5 = 0$ with the standard form $ax^2 + bx + c = 0$,we get $a = \ldots \ldots \ldots \ldots$.
Easy
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