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).

Algebra ->  Polynomials-and-rational-expressions -> 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).       Log On


   

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(39616) About Me  (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.

p%28x%29=a%28x-1%29%5E2%28x-4%29%28x-10%29
You should find that a%3C0, and get its value using p%280%29=-2.

(approximately, a=-%281%2F20%29, but let x=0 and solve for a to be sure.)