Question

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

\(2x^2+x-4=0\)

Answer 1

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

\((a+b)^2=a^2+2ab+b^2\)

\(2x^2+x-4=0\)

⇒ x² + x/2 – 2 = 0 

⇒ x² + 2 × 1/4 × x + (1/4)² - (1/4)² – 2 = 0

⇒ (x + 1/4)² = 33/16

⇒ x + 1/4 =  √33/4

\(\Rightarrow x=\frac{\sqrt{33}-1}{4},\frac{-\sqrt{33}-1{}}{4}\)