Question

Find all the zeroes of each function y=x^3-4x^2+9x-36

Answer 1

Given data:

The given expression is y=x^3-4x^2+9x-36.

Substitute 0 for y in the given expression.

`\begin{gathered} 0=x^3-4x^2+9x-36 \\ 0=x^2(x-4)+9(x-4) \\ 0=(x-4)(x^2+9) \\ 0=(x-4)(x+3i)(x-3i) \\ x=4,\text{ -3i, +3i} \end{gathered}`

Thus, the value of x is 4, -3i, and +3i.