Question

For what values of a, the quadratic equation 9x² – 3ax + 1 = 0 has real and equal roots?

Answer 1

Given: 9x² – 3ax + 1 = 0

Step-wise calculation:

1. For real and equal roots the discriminant must be zero:

D = b² – 4ac = 0

2. Here A = 9, B = –3a, C = 1

So, D = (–3a)² – 4 × 9 × 1 

= 9a² – 36

= 9(a² – 4)

3. Set D = 0

⇒ 9(a² – 4) = 0 

⇒ a² – 4 = 0

⇒ a² = 4 

⇒ a = ±2

The quadratic has real and equal roots for a = 2 or a = –2.