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Algebra/complex zeros

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Expert: - 1/27/2011


Question
Find the complex zeros of F(x). Write F in factored form.

F(x)=x^3-3x^2+12x-10

Answer
It can be seen that if 1 is put in, we get F(1) = 1 - 3 + 12 - 10 = 0.
Therefore one of the factors is x-1.

Taking out the x-1 gives F(x) = (x-1)(x^2 - 2x + 10).
Use the quadratic equation to find the factors a and b of x^2 - 2x + 10.
The answer would then be F(x) = (x-1)(x-a)(x-b).

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