Question
Find the value of the constant "k" for which the equation 2x^2 + (k+3)x + 2k =0 has equal roots
Answers
GPT 3.5
For the equation to have equal roots, the discriminant should be equal to zero.
So, we have:
(k + 3)^2 - 4(2)(2k) = 0
k^2 + 6k + 9 - 16k = 0
k^2 - 10k + 9 = 0
(k - 9)(k - 1) = 0
k = 9 or k = 1
Therefore, the constant value of "k" for which the equation has equal roots is 9 or 1.
So, we have:
(k + 3)^2 - 4(2)(2k) = 0
k^2 + 6k + 9 - 16k = 0
k^2 - 10k + 9 = 0
(k - 9)(k - 1) = 0
k = 9 or k = 1
Therefore, the constant value of "k" for which the equation has equal roots is 9 or 1.