Question

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x² – 7x + 3  = 0

Answer 1

2x² – 7x + 3 = 0

⇒ 2x² – 7x = - 3

On dividing both sides of the equation by 2, we get

`⇒ x^2 – (7x)/2 = -3/2`

`⇒ x^2 – 2 × x × 7/4 = -3/2`

On adding (7/4)² to both sides of equation, we get

`⇒ (x)^2 - 2 × x × 7/4 + (7/4)^2 = (7/4)^2 - 3/2`

`⇒ (x - 7/4)^2 = 49/16 - 3/2`

`⇒ (x - 7/4)^2 = 25/16`

`⇒ (x - 7/4) = ± 5/4`

`⇒ x = 7/4 ± 5/4`

`⇒ x = 7/4 + 5/4 or x = 7/4 - 5/4`

`⇒ x = 12/4 or x = 2/4`

⇒ x = 3 or 1/2