Question

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x² + x + 4 = 0

Answer 1

2x² + x + 4 = 0

⇒ 2x² + x = -4

On dividing both sides of the equation, we get

`⇒ x^2 + 1/(2x) = 2`

`⇒ x^2 + 2 × x × 1/4 = -2`

On adding (1/4)² to both sides of the equation, we get

`⇒ (x)^2 + 2 × x × 1/4 + (1/4)^2 = (1/4)^2 - 2 `

`⇒ (x + 1/4)^2 = 1/16 - 2`

`⇒ (x + 1/4)^2 = -31/16`

However, the square of number cannot be negative.

Therefore, there is no real root for the given equation