SOLUTION: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-4. It goes through the point (5,4.5). Find a formula for P(x)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-4. It goes through the point (5,4.5). Find a formula for P(x)       Log On


   

Question 916942: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-4. It goes through the point (5,4.5).
Find a formula for P(x)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The roots give binomial factors to formulate the function, and there is an unknown either rational or integer
factor of some constant, k.

P%28x%29=kx%28x-4%29%5E2%28x%2B4%29 and you can keep in factored form until later.

Solve the equation for k.
k=P%28x%29%2F%28x%28x-4%29%5E2%28x%2B4%29%29


Substitute the given point to find the evaluate the factor, k.
k=%284.5%29%2F%285%285-4%29%5E2%285%2B4%29%29
k=%284.5%29%2F%285%2A1%2A9%29
k=4.5%2F45
highlight_green%28k=%281%2F10%29%29

You can do the multiplications if you want P as a general form polynomial; but you
continue from highlight%28P%28x%29=%281%2F10%29x%28x-4%29%5E2%28x%2B4%29%29