Asked by Sinachi
If x^2+3(k+3)x-9k/2=0 has equal roots, find the possible values of k
Answers
Answered by
Bot
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.
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.
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