# Math Help - equation

1. ## equation

Y=X³+12X²+36X is used to find solutions of the equation X³+12X²+36X=k for various values

The maximum point is (-6,0)
The minimum point is (-2,-32)
1) Verify the point (-8,-32) is on the graph
2) Find the number of real roots of the equation when k is:
i) 0
ii) 20
iii) -20
iv) -40
3) For what value of k does the equation have three real roots? What can you say about these roots?
any help would be fab

2. I do not understand your question. Using your given polynomial, the point (-8, -32) is not a valid coordinate of the graph.

3. (−8,−32) is on the graph $y = x^3+12x^2+36x$.

So, the y-value of the local maximum is 0 and the y-value of the local minimum is is −32. What this means is that for −32 ≤ k ≤ 0, the equation $x^3+12x^2+36x=k$ has three real roots. (In the case k = −32 or 0, two of the real roots are repeated.) For k < −32 or k > 0, the equation $x^3+12x^2+36x=k$ has only one real root.