Question

Find the values of k for which the quadratic equation 3x² + kx + 3 = 0 has real and equal roots?

Answer 1

Given: 3x² + kx + 3 = 0

Step-wise calculation:

1. Compare with ax² + bx + c = 0:

a = 3, b = k, c = 3

2. Discriminant D = b² – 4ac

= k² – 4(3)(3)

= k² – 36 

For real and equal roots we require D = 0.

3. Set D = 0:

k² – 36 = 0

⇒ k² = 36

⇒ k = ±6

4. The equal root is `x = (-b)/(2a) = (-k)/(6)`. 

Thus for k = 6 the double root is x = –1 and for k = –6 the double root is x = 1.