SOLUTION: Find the polynomial of degree 4 with integer coefficient with zeros i, 3, and −3, and with P(−1) = 36.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the polynomial of degree 4 with integer coefficient with zeros i, 3, and −3, and with P(−1) = 36.      Log On


   

Question 1068199: Find the polynomial of degree 4 with integer coefficient with zeros i, 3, and −3, and with
P(−1) = 36.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the polynomial of degree 4 with integer coefficient with zeros i, 3, and −3, and with
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Since the coefficients are integers, -i is also a zero.
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f(x) = a(x+i)(x-i)(x+3)(x-3)
f(x) = a(x^2+1)(x^2-9)
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Using P(−1) = 36, find "a".
36 = a(1+1)(1-9)
36 = a(2)(-8)
a = 36/-16
a = -9/4
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f(x) = (-9/4)(x^4-8x^2-9)
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Cheers,
Stan H.
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