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

Asked by Topperlearning User 11th September 2017, 10:47 AM
Answered by Expert
Answer:

(k + 4)x2 + (k + 1)x + 1 = 0

a = k + 4, b = k + 1, c = 1

For equal roots, dicriminant, D = 0

b2 - 4ac = 0

(k + 1)2 - 4(k + 4) ×1 = 0

k2 + 2k + 1 - 4k - 16 = 0

k2 - 2k - 15 = 0

k2 - 5k + 3k - 15 = 0

k(k - 5) + 3(k - 5) = 0

(k - 5) (k + 3) = 0

k = 5 or k = -3

Thus, for k = 5 or k = - 3, the given quadratic equation has equal roots.

Answered by Expert 11th September 2017, 12:47 PM
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