Question 613232: Find an equation of a polynomial function of least degree having complex zeros: -i & -2i. X-intercept: (2,0). Y-intercept: (0,-2)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find an equation of a polynomial function of least degree having complex zeros: -i & -2i. X-intercept: (2,0). Y-intercept: (0,-2)
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If I assume the coefficients of the polynomial function
are Real Numbers, then i and 2i are also zeros.
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f(x) = a(x-i)(x+i)(x-2i)(x+2i)(x-2)
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To solve for "a", use the point (0,-2)
-2 = a(-i)(i)(-2i)(2i)(-2)
1 = a(1)(4)
a = 1/4
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Equation:
f(x) = (1/4)(x^2+1)(x^2+4)(x-2)
Degree: 5
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Cheers,
Stan H.
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