Question

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

kx² + kx + 1 = –4x² – x

Answer 1

Given: kx² + kx + 1 = –4x² – x

Step-wise calculation:

1. Bring all terms to one side:

(k + 4)x² + (k + 1)x + 1 = 0

2. For equal (repeated) roots the discriminant must be zero: 

b² – 4ac = 0

3. Compute the discriminant:

(k + 1)² – 4(k + 4)(1) = 0

k² + 2k + 1 – 4k – 16 = 0

k² – 2k – 15 = 0

4. Factor:

(k – 5)(k + 3) = 0 

⇒ k = 5 or k = –3