How do you find all the zeros of $f(x) = x^3-x^2+25x-25$ ?

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Answer 1 · 2016-04-25T06:24:57

$x = 1, +-5 i$ .

Sum of the coefficients = 0. So, 1 is a root.

One factor of the cubic is $(x - 1).$ .

The other quadratic factor is readily seen as $(x^2+5^2)$ .

$(x^2+5^2) = 0$ gives the other two roots as $+- 5 i$ .

How do you find all the zeros of f(x) = x^3-x^2+25x-25 f(x) = x^3-x^2+25x-25?