SOLUTION: The polynomial of degree 4, P(x) has a root multiplicity 2 at x=4 and roots multiplicity 1 at x=0 and x=-1 and it goes through the point (5, 24). Find a formula for P(x). P(x)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial of degree 4, P(x) has a root multiplicity 2 at x=4 and roots multiplicity 1 at x=0 and x=-1 and it goes through the point (5, 24). Find a formula for P(x). P(x)      Log On


   

Question 1169888: The polynomial of degree 4, P(x) has a root multiplicity 2 at x=4 and roots multiplicity 1 at x=0 and x=-1 and it goes through the point (5, 24).
Find a formula for P(x).
P(x)=
Answer by MathLover1(20850) About Me  (Show Source):
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given:
x%5B1%5D=x%5B2%5D=4
x%5B3%5D=0
x%5B4%5D=-1
and it goes through the point (5,24)
P%28x%29=a%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
P%28x%29=a%28x-4%29%28x-4%29%28x-0%29%28x-%28-1%29%29
P%28x%29=a%28x-4%29%28x-4%29%28x%29%28x%2B1%29
P%28x%29=a%28x%5E2+-+8x+%2B+16%29%28x%5E2%2Bx%29
P%28x%29=a%28x%5E4+-+7x%5E3+%2B+8x%5E2+%2B+16x%29.....use given point (5,24) to calculate a
24=a%285%5E4+-+7%2A5%5E3+%2B+8%2A5%5E2+%2B+16%2A5%29
24=a%2830%29
a=24%2F30
a=4%2F5
then
P%28x%29=%284%2F5%29%28x%5E4+-+7x%5E3+%2B+8x%5E2+%2B+16x%29
P%28x%29=%284x%5E4%29%2F5+-%2828x%5E3%29%2F5+%2B%2832x%5E2%29%2F5+%2B%2864x%29%2F5