Asked by alice
The quadratic equation $x^2+4mx+m = 2x - 6$ has exactly one real root. Find the positive value of $m$.
Answers
Answered by
oobleck
wrong again.
If it has one root, the discriminant is zero.
x^2+4mx+m = 2x - 6
x^2+(4m-2)x+(m-6) = 0
so we need (4m-2)^2-4(m+6) = 0
(2m-1)^2 - (m+6) = 0
4m^2-5m-5 = 0
m = (5±√105)/8
so the positive value is (5+√105)/8
If it has one root, the discriminant is zero.
x^2+4mx+m = 2x - 6
x^2+(4m-2)x+(m-6) = 0
so we need (4m-2)^2-4(m+6) = 0
(2m-1)^2 - (m+6) = 0
4m^2-5m-5 = 0
m = (5±√105)/8
so the positive value is (5+√105)/8
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.