Find the roots of the following quadratic (if they exist) by the metho

1.	Find the roots of the following quadratic (if they exist) by the method of completing the square.\(2x^2+x-4=0\)
Answer» 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 \(\Rightarrow x=\frac{\sqrt{33}-1}{4},\frac{-\sqrt{33}-1{}}{4}\)

Find the roots of the following quadratic (if they exist) by the method of completing the square.\(2x^2+x-4=0\)

Answer»

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

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