SOLUTION: Hello im am really struggling with this question,can you please help me,im desperate and this is my last option. The question says :DETERMINE THE VALUE(S) OF K FOR WHICH -2X^3 - 3X

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Question 339039: Hello im am really struggling with this question,can you please help me,im desperate and this is my last option. The question says :DETERMINE THE VALUE(S) OF K FOR WHICH -2X^3 - 3X^2 +12X +20=K HAS 3 REAL ROOTS .thank you.plz help plz
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
It would be tedious to guess and check so we will use the discriminant.
The discriminant for a cubic is considerably longer than that for a quadratic.
It is:
b%5E2%2Ac%5E2-4ac%5E3-4b%5E3d-27a%5E2d%5E2%2B18abcd
In order for there to be three real roots, the discriminant must be > 0.
Letting a=-2 b=-4 c=12 d=20-k, and
making the subs it whittles down to
-108k%5E2%2B2916k%3E0
k%28k-27%29%3C0
k%3C27
It has three real roots if k is less than 27.