Question

If the equation x2 + 2(k+2)x + 9k = 0 has equal roots, find k?

Answer 1

try hit and trial method. it satisfies for K=1 which gives X=-3 equal roots

Answer 2

Hi!

x² + 2[ k + 2]x + 9k = 0

a = 1 , b = 2[k+2]  , c = 9k

As the equation has equal roots,
b² - 4ac = 0

that is ,

{ 2[k+2] }² - 4 × 9k = 0

4 [ k+2]² - 36k = 0

4 [ k² + 4k + 4 ] - 36k = 0

4 k² + 16k + 16 -36k = 0
4 k²  - 20k + 16 = 0

Dividing by 4 ,

k² - 5k + 4 = 0
(k - 4) (k - 1) =0

k = 4 , k = 1