Check whether the equation 5x^2 – 6x – 2 = 0 has real roots
Check whether the equation 5x2 – 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 = b2 – 4ac
= 36 – 4 × 5 × (–2)
= 76 > 0
So, the given equation has two distinct real roots.
5x2 – 6x – 2 = 0
Multiplying both sides by 5.
(5x)2 – 2 × (5x) × 3 = 10
(5x)2 – 2 × (5x) × 3 + 32 = 10 + 32
(5x – 3)2 = 19
5x – 3 = ±√19
x = (3 ± √19)/5
Verification:
