Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

$x^2 - 4ax + 4a^2 - b^2 = 0$

Given:

Given quadratic equation is $x^2 - 4ax + 4a^2 - b^2 = 0$.

To do:

We have to find the roots of the given quadratic equation.

Solution:

$x^2 - 4ax + 4a^2 - b^2 = 0$

$x^2-2\times 2ax +(2a)^2=(b)^2$

$(x-2a)^2=b^2$   (Since $(a-b)^2=a^2-2ab+b^2$)

$x-2a=\pm \sqrt{b^2}$

$x-2a=\pm b$

$x-2a=b$ or $x-2a=-b$

$x=2a+b$ or $x=2a-b$

The values of $x$ are $2a+b$ and $2a-b$.

Tutorialspoint

Updated on: 10-Oct-2022

48 Views

Kickstart Your Career

Get certified by completing the course

Get Started