Question 1093636: The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=−4, The y-intercept is y=−51.2. Find a formula for P(x).
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! From the roots, the factors are (x-4)^2*(x+4)
when x=0, y=-51.2
(x^2-8x+16)(x+4)=x^3-4x^2-16x+64
but when x=0, y=-51.2
a*(x^3-4x^2-16x+64), when x=0, 64a=-51.2. Therefore, a=-0.8
The equation is -0.8x^3+3.2x^2+12.8x-51.2
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=−4, The y-intercept is y=−51.2. Find a formula for P(x).
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P(x) = A(x-4)^2(x+4)
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Solve for "A" using (0,-51.2)
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P(0) = -51.2
-51.2 = A(0-4)^2(0+4)
-51.2 = A*16*4
-51.2 = A*64
A = -51.2/64
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Ans: P(x) = (-51.2/64)(x-4)^2(x+4)
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Cheers,
Stan H.
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