SOLUTION: The function p is a fourth-degree polynomial with x-intercepts 1, 4, and 10 and y-intercept -2. If p(x) is positive only on the interval (4, 10), find p(x).

Question 916646: The function p is a fourth-degree polynomial with x-intercepts 1, 4, and 10 and y-intercept -2. If p(x) is positive only on the interval (4, 10), find p(x).
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The description means that p crosses the x-axis at 4 and 10; but p only touches (does not cross) the x-axis at 1. THIS is the root which has multiplicity of 2.

You should find that , and get its value using .

(approximately, , but let x=0 and solve for a to be sure.)

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