SOLUTION: The function p is a fourth-degree polynomial with x-intercepts 1.5, 3, and 9 and y-intercept -3. If p(x) is positive only on the interval (3, 9), find p(x) Please explain, Than

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The function p is a fourth-degree polynomial with x-intercepts 1.5, 3, and 9 and y-intercept -3. If p(x) is positive only on the interval (3, 9), find p(x) Please explain, Than      Log On


   

Question 911776: The function p is a fourth-degree polynomial with x-intercepts 1.5, 3, and 9 and y-intercept -3. If p(x) is positive only on the interval (3, 9), find p(x)
Please explain,
Thank you
Found 2 solutions by ichigo449, josgarithmetic:
Answer by ichigo449(30) About Me  (Show Source):
You can put this solution on YOUR website!
You are given roots so multiply the corresponding linear factors and use the positivity condition to find the coefficients.

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
The description will ultimately give a detail about multiplicity of one of the factors.

As a start the function is something like p%28x%29=k%28x-3%2F2%29%28x-3%29%28x-9%29 and using the point (3,9) means p%283%29=9. This detail helps you to find the value of k.
p(x) as written there is INCOMPLETE, because you want DEGREE 4, and need to decide which factor gets the power of 2.

Also p has the point (0,-3), the given y-intercept. You can distinguish that, from this and general qualities about polynomial functions, k%3E0.

Can you pick the correct multiplicities of each binomial factor, and get the value of k?