Question

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

x² – 2kx + 7k – 12 = 0

Answer 1

Given: x² – 2kx + 7k – 12 = 0

Step-wise calculation:

1. a = 1, b = –2k, c = 7k – 12.

2. Discriminant D = b² – 4ac

= (–2k)² – 4(1)(7k – 12)

= 4k² – 28k + 48

3. For equal (repeated) roots set D = 0:

4k² – 28k + 48 = 0

Divide by 4

k² – 7k + 12 = 0

4. Factor: (k – 3)(k – 4) = 0

k = 3 or k = 4

The equation has equal roots when k = 3 or k = 4. For k = 3 the root is x = 3; for k = 4 the root is x = 4.