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=−3 Find a possible formula for P

Algebra ->  Functions -> 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=−3 Find a possible formula for P      Log On


   



Question 997792: 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=−3
Find a possible formula for 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%5B1%5D=x%5B2%5D=2 and x%5B3%5D=x%5B4%5D=0, and a root of multiplicity 1 at x%5B5%5D=-3
a possible formula for P%28x%29 is:
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...since x%5B1%5D=x%5B2%5D=2 and x%5B3%5D=x%5B4%5D=0, we can write it like this
P%28x%29=%28x-x%5B1%5D%29%5E2%28x-x%5B3%5D%29%5E2%28x-x%5B5%5D%29....plug in given values
P%28x%29=%28x-2%29%5E2%28x-0%29%5E2%28x-%28-3%29%29
P%28x%29=%28x%5E2-4x%2B4%29%28x%5E2%29%28x%2B3%29
P%28x%29=%28x%5E4-4x%5E3%2B4x%5E2%29%28x%2B3%29
P%28x%29=x%5E5-4x%5E4%2B4x%5E3%2B3x%5E4-12x%5E3%2B12x%5E2
P%28x%29=x%5E5-x%5E4-8x%5E3%2B12x%5E2