Question

x^2+ 2(k + 2)x+ 9 = 0 has equal roots,
If the equation
then find the values of k.​

Answer 1

Answer:

x^2+ 2(k + 2)x+ 9 = 0

a = 1, b = 2(k + 2), c = 9

Given equation has equal roots

Therefore, b^2 - 4ac = 0

[2(k + 2)]^2 - 4(1)(9) = 0

4(k^2 + 4k + 4) -36 = 0

4k^2 + 16k + 16 - 36 = 0

4k^2 + 16k - 20 = 0

k^2 + 4k - 5 = 0 [ divide each term by 4]

(k + 5)(k - 1) = 0

[ Zeroth product rule ]

=> k = -5 or 1