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
Dec 19th 2007, 10:48 AM
I do not understand your question. Using your given polynomial, the point (-8, -32) is not a valid coordinate of the graph.
Dec 19th 2007, 12:45 PM
(−8,−32) is on the graph .
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 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 has only one real root.