Question

Find the values of k for which the following equation has equal roots:

9x² + kx + 1 = 0

Answer 1

Given: 9x² + kx + 1 = 0 so a = 9, b = k, c = 1

Step-wise calculation:

1. Discriminant Δ = b² – 4ac 

= k² – 4 × 9 × 1 

= k² – 36

2. For equal roots Δ = 0

⇒ k² – 36 = 0

⇒ k² = 36

⇒ k = ±6

3. The common root is `x = (-b)/(2a)`

= `(-k)/(2 xx 9)` 

= `(-k)/18` 

Thus:

If k = 6, `x = −6/18 = −1/3` (Double root).

If k = −6, `x = 6/18 = 1/3` (Double root).

k = 6 or k = –6. 

Corresponding equal roots: `–1/3` for k = 6 and `1/3` for k = –6.