SOLUTION: Construct a polynomial with the following properties: third degree, real coefficients, y-intercept is -52, zeros are -1, and 5+i.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Construct a polynomial with the following properties: third degree, real coefficients, y-intercept is -52, zeros are -1, and 5+i.       Log On


   

Question 915235: Construct a polynomial with the following properties: third degree, real coefficients, y-intercept is -52, zeros are -1, and 5+i.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A polynomial with real coefficients has roots that are complex conjugates pairs.
So then,
f%28x%29=a%28x%2B1%29%28x-%285%2Bi%29%29%28x-%285-i%29%29
f%28x%29=a%28x%2B1%29%28x%5E2-10x%2B26%29
f%28x%29=a%28x%5E3-9x%5E2%2B16x%2B26%29
Then, when x=0, f%280%29=-52
a%280-0%2B0%2B26%29=-52
a=-2
.
.
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f%28x%29=-2x%5E3%2B18x%5E2-32x-52%29