SOLUTION: The degree three polynomial f(x) with real coefficients and leading coefficient 1 has -3 and 4i among its roots. Express f(x)as a porduct of linear and quadratic polynomials with r

Question 102562This question is from textbook Algebra and Trigonometry
: The degree three polynomial f(x) with real coefficients and leading coefficient 1 has -3 and 4i among its roots. Express f(x)as a porduct of linear and quadratic polynomials with real coefficients. This question is from textbook Algebra and Trigonometry

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The degree three polynomial f(x) with real coefficients and leading coefficient 1 has -3 and 4i among its roots. Express f(x)as a porduct of linear and quadratic polynomials with real coefficients.
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If f(x) has real coefficients and 4i is a root, then -4i is also a root.
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f(x) = (x+3)(x-4i)(x+4i)
f(x) = (x+3)(x^2+16)
f(x) = x^3+3x^2+16x+48
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Cheers,
Stan H.
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