Question

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

Answer 1

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)`