Question

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

\(4x^2-4ax+4a^2-b^2=0\)

Answer 1

We have to make the quadratic equation a perfect square if possible or sum of perfect square with a constant.

(a + b)² = a² + 2ab + b²

^{\(x^2-4ax+4a^2-b^2 = 0\)}

⇒ x² – 2 × 2ax + 4a² = b² 

⇒ (x – 2a)² = b² 

⇒ x – 2a = ±b 

⇒ x = 2a + b, 2a – b