Question

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

x² - 4ax + 4a² - b² = 0

Answer 1

We have to find the roots of given quadratic equation by the method of completing the square. We have,

x² - 4ax + 4a² - b² = 0

Now shift the constant to the right hand side,

x² - 4ax = b² - 4a²

Now add square of half of coefficient of x on both the sides,

x² - 2(2a)x + (2a)² = b² - 4a² + (2a)²

We can now write it in the form of perfect square as,

(x - 2a)² = b²

Taking square root on both sides,

`(x-2a)=sqrt(b^2)`

So the required solution of x,

x = 2a ± b

x = 2a + b, 2a - b