Check whether the equation 5x^{2} – 6x – 2 = 0 has real roots and if it has, find them by the method of completing the square. Also verify that roots obtained satisfy the given equation.

### Answer

Discriminant = b^{2} – 4ac

= 36 – 4 × 5 × (–2)

= 76 > 0

So, the given equation has two distinct real roots.

5x^{2} – 6x – 2 = 0

Multiplying both sides by 5.

(5x)^{2} – 2 × (5x) × 3 = 10

(5x)^{2} – 2 × (5x) × 3 + 3^{2} = 10 + 3^{2}

(5x – 3)^{2} = 19

5x – 3 = ±√19

x = (3 ± √19)/5

Verification: