For what values of k, are the roots of the quadratic equation: (k + 4) x2 + (k + 1) x + 1 = 0 equal?

Question

Philoid · Accepted Answer

For roots to be equal, discriminant should be zero i.e.,

D = b² – 4ac

⸫ D = (k + 1)² – 4 (k + 4) (1) = 0

⇒ k² + 2k + 1 – 4k – 16 = 0

⇒ k² – 2k – 15 = 0

[By splitting the middle term]

⇒ k² – 5k + 3k – 15 = 0

⇒ k (k – 5) + 3 (k – 5) = 0

⇒ (k – 5) (k + 3) = 0

⇒ k – 5 = 0 and k + 3 = 0

⸫ k = 5 or k = -3

For what values of k, are the roots of the quadratic equation: (k + 4) x² + (k + 1) x + 1 = 0 equal?