SOLUTION: Find the polynomial equation, given the solutions and degree: solutions: -2, 1-4i degree: 3

Question 1055073: Find the polynomial equation, given the solutions and degree:
solutions: -2, 1-4i
degree: 3
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the polynomial equation, given the solutions and degree:
solutions: -2, 1-4i
degree: 3
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Since the degree is 3, 1+4i is also a solution
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f(x) = (x-3)(x-(1+4i))(x-(1-4i))
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f(x) = (x-3)((x-1)-4i)((x-1)+4i)
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f(x) = (x-3)[(x-1)^2+16]
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f(x) = (x-3)(x^2-2x+ 17)
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f(x) = x^3 - 2x^2-3x^2 + 17x + 6x - 51
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f(x) = x^3 - 5x^2 + 23x - 51
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Cheers,
Stan H.
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