Question

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 

Answer 1

check the values of b^2-4ac in the equation ax^2+bx+c, i.e., 5x^2 – 6x – 2 = 0

 b^2-4ac = (-6)^2-4(5)(-2)
               =36+40
               =76

Therefore the equation has two real roots since b^2-4ac > 0

NOTE IF:
1. b^2 −4ac < 0 There are no real roots.

2. b^2 −4ac = 0 There is one real root.

3. b^2 −4ac > 0 There are two real roots

Answer 2

Discriminant = b^2 – 4ac,

a = 5, b = – 6, c = – 2

= 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 + 32

(5x – 3)^2 = 19

5x – 3 = ±√19

x =  3 ± √19  ÷ 5