SOLUTION: Dear Sir/Madam, Good day! Kindly help me with this problem, I sent almost the same problem but committed an error of tying the wrong value. Here it goes... Find the value of k

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Dear Sir/Madam, Good day! Kindly help me with this problem, I sent almost the same problem but committed an error of tying the wrong value. Here it goes... Find the value of k       Log On


   

Question 767460: Dear Sir/Madam,
Good day! Kindly help me with this problem, I sent almost the same problem but committed an error of tying the wrong value. Here it goes...
Find the value of k so that the equation 3x^2-4kx+k =0 will have real roots. Thank you very much for your help!
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
Find the value of k so that the equation 3x%5E2-4kx%2Bk+=0 will have real roots
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A:
The quadratic equation ax%5E2+%2B+bx+%2B+c+=+0 have real roots if the discriminant b%5E2-4ac is greater than or equal to zero.
In 3x%5E2-4kx%2Bk+=0, a = 3, b = -4k and c = k.
The discriminant is equal to %28-4k%29%5E2+-+4%283%29%28k%29 = 16k%5E2+-+12k.
16k%5E2+-+12k ≥ 0
4k(4k - 3) ≥ 0
Using sign test
k ≤ 0 OR k ≥ 3/4
In interval notation: (-∞, 0] ∪ [ 3%2F4, ∞)