SOLUTION: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and. Root of multiplicity 1 at x=-4. The y intercept is y=-9.6 Find a formula for P(x) P(x)=

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and. Root of multiplicity 1 at x=-4. The y intercept is y=-9.6 Find a formula for P(x) P(x)=      Log On


   

Question 1182615: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and. Root of multiplicity 1 at x=-4. The y intercept is y=-9.6
Find a formula for P(x)
P(x)=
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=a%28x-2%29%5E2%28x%2B4%29
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a%28x-2%29%5E2%28x%2B4%29=P%28x%29
a=%28-9.6%29%2F%28%28%28-2%29%28-2%29%284%29%29%29-------using the y-intercept information
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


In the factored form of the polynomial, a root of multiplicity 2 at x=2 means two linear factors of (x-2); a root of multiplicity 1 at x=-4 means one linear factor of (x+4). So the polynomial in factored form is of the form

P%28x%29=a%28x-2%29%5E2%28x%2B4%29

To determine the constant factor a, use the given fact that the y-intercept P(0) is -9.6:

P%280%29=a%28-2%29%5E2%284%29=-9.6
16a=-9.6
a=-9.6%2F16=-0.6

ANSWER: P%28x%29=-0.6%28x-2%29%5E2%28x%2B4%29