SOLUTION: The polynomial of degree 5, P ( x ) has leading coefficient 1, has roots of multiplicity 2 at x = 2 and x = 0 , and a root of multiplicity 1 at x = − 2 Find the formula for P ( x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial of degree 5, P ( x ) has leading coefficient 1, has roots of multiplicity 2 at x = 2 and x = 0 , and a root of multiplicity 1 at x = − 2 Find the formula for P ( x      Log On


   



Question 1170234: The polynomial of degree 5, P ( x ) has leading coefficient 1, has roots of multiplicity 2 at x = 2 and x = 0 , and a root of multiplicity 1 at x = − 2 Find the formula for P ( x ) .
P(x)=

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
The polynomial of degree 5,
P%28x%29 has leading coefficient 1,
has roots of multiplicity 2 at x+=+2+and x+=+0 ,so roots are:
x%5B1%5D+=+2
x%5B2%5D+=+2
x%5B3%5D+=+0
x%5B4%5D+=+0
and
also given a root of multiplicity 1 at x+=+-2+ =>
x%5B5%5D+=-2

P%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29%28x-x%5B5%5D%29
P%28x%29=%28x-2%29%28x-2%29%28x-0%29%28x-0%29%28x-%28-2%29%29
P%28x%29=%28x-2%29%28x-2%29%28x%29%28x%29%28x%2B2%29
P%28x%29=x%5E2%28x-2%29%28x%5E2-2%5E2%29
P%28x%29=%28x%5E3-2x%5E2%29%28x%5E2-4%29
P%28x%29=x%5E5+-+2x%5E4+-+4x%5E3+%2B+8x%5E2