- Trending Categories
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find the roots of the following quadratic equation:
$x^{2} -3\sqrt {5}\ x+10=0$
Given: The expression: $x^{2} -3\sqrt{5} \ x+10=0$
To do: To find the roots of the given quadratic equation.
Solution: We know that for a quadratic equation $ax^{2} +bx+c=0$
$x=\frac{-b\pm \sqrt{b^{2} -4ac}}{2a}$
On comparing it to the given quadratic equation $a=1,b=-3\sqrt{5} \ and\ c=10$
On substituting these values of $\displaystyle a,\ b\ and\ c$
$x=\frac{-( -3\surd 5) \pm \sqrt{( -3\surd 5)^{2} -4\times 1\times 10}}{2\times 1}$
$x=\frac{3\sqrt{5} \pm \sqrt{( 45-40)}}{2}$
$x=\frac{\left( 3\sqrt{5} \pm \sqrt{5}\right)}{2}$
If $x=\frac{\left( 3\sqrt{5} +\sqrt{5}\right)}{2}$
$\Rightarrow x=\frac{4\sqrt{5}}{2} $
$\Rightarrow x=2\sqrt{5}$
If $x=\frac{\left( 3\sqrt{5} -\sqrt{5}\right)}{2}$
$\Rightarrow x=\frac{\left( 2\sqrt{5}\right)}{2}$
$\Rightarrow x=\sqrt{5}$
$\therefore x=2\sqrt{5}, \ \sqrt{5}$
- Related Articles
- Find the roots of the quadratic equation $\sqrt{2}x^{2}+7x+5\sqrt{2}=0$.
- Find the roots of the following quadratic equations by the factorisation method:\( 3 x^{2}+5 \sqrt{5} x-10=0 \)
- Find the roots of the following quadratic equations by the factorisation method:\( 3 \sqrt{2} x^{2}-5 x-\sqrt{2}=0 \)
- Find the roots of the quadratic equations by using the quadratic formula in each of the following:\( x^{2}-3 \sqrt{5} x+10=0 \)
- Solve the following quadratic equation by factorization: $3\sqrt{5}x^2+25x-10\sqrt5=0$
- Solve the following quadratic equation for x:$4\sqrt{3} x^{2} +5x-2\sqrt{3} =0$
- Find the roots of the following quadratic equations by factorisation:$\sqrt{2}x^2 + 7x + 5\sqrt{2} = 0$
- Solve the following quadratic equation by factorization: $\sqrt{3}x^2-2\sqrt{2}x-2\sqrt3=0$
- Find the roots of the following quadratic equations by the factorisation method:\( 2 x^{2}+\frac{5}{3} x-2=0 \)
- Find the roots of the following quadratic equations by the factorisation method:\( \frac{2}{5} x^{2}-x-\frac{3}{5}=0 \)
- Find the roots of the quadratic equations by using the quadratic formula in each of the following:\( 2 x^{2}-3 x-5=0 \)
- Solve the following quadratic equation by factorization: $\sqrt{2}x^2+7x+5\sqrt2=0$
- Find the discriminant of the quadratic equation $3\sqrt{3}x^2+10x+\sqrt{3}$.
- Solve the following quadratic equation by factorization: $x^2-(\sqrt{2}+1)x+\sqrt2=0$
- If the quadratic equation $px^{2}-2\sqrt{5}x+15=0$ has two equal roots, then find the value of $p$.
Advertisements