If x^2+3(k+3)x-9k/2=0 has equal roots, find the possible values of k

Answer 1

If the equation has equal roots, then the discriminant (b^2-4ac) of the quadratic equation must be zero.

Therefore, (3(k+3))^2 - 4(1)(-9k/2) = 0

Simplifying this equation, we get:

9(k^2 + 6k + 9) + 18k = 0

Simplifying further, we get:

9k^2 + 72k + 81 = 0

Dividing both sides by 9, we get:

k^2 + 8k + 9 = 0

Factoring this quadratic equation, we get:

(k+1)(k+9) = 0

Therefore, the possible values of k are -1 and -9.