SOLUTION: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 1 and a root of multiplicity 1 at x = −1. The y-intercept is y = −0.6. Find a formula for P(x).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 1 and a root of multiplicity 1 at x = −1. The y-intercept is y = −0.6. Find a formula for P(x).      Log On


   

Question 1176955: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 1 and a root of multiplicity 1 at x = −1. The y-intercept is y = −0.6.
Find a formula for P(x).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a root of multiplicity 2 at x%5B1%5D+=+1 =>%28x-1%29%5E2
a root of multiplicity 1 at+x%5B2%5D+=+-1=>%28x%2B1%29
y-intercept is y+=+-0.6
P%28x%29=a%28x-1%29%5E2%2A%28x%2B1%29+.........y-intercept is y+=+-0.6, or point (0,1), use it to find a
-0.6=a%280-1%29%5E2%2A%280%2B1%29
-0.6=a%281+%29%281+%29
a=-0.6
then
P%28x%29=-0.6%28x%5E2-2x%2B1%29%2A%28x%2B1%29
P%28x%29=-0.6%28x%5E3+-+x%5E2+-+x+%2B+1%29
P%28x%29=-0.6x%5E3+%2B0.6x%5E2+%2B0.6x+-0.6