How do you find all zeros of the function $f(x) = x^3 - 4x^2-9x+36$ ?

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Answer 1 · 2016-06-08T16:11:32

1st Method

Check if the divisors of the constant term $36$ are roots of the equation.In our case $4,-3,3$ are roots of the equation hence

$f(x)=x^3 - 4x^2-9x+36=(x-4)(x-3)(x+3)$

2nd Method

We can easily factorise this as follows

$x^3-4x^2-9x+36=x(x^2-9)-4(x^2-9)=(x^2-9)(x-4)=(x-3)(x+3)(x-4)$

How do you find all zeros of the function f(x) = x^3 - 4x^2-9x+36f(x) = x^3 - 4x^2-9x+36?