Chapter 4.4, Problem 2MCQ

To determine

To state: The number of complex roots of $x^3-11x^2+30x=0$ and find the roots.

Answer to Problem 2MCQ

  $x=0,5,6$

Explanation of Solution

Given information: $x^3-11x^2+30x=0$

Calculation:

  $\begin{array}{l}{x}^3-11x^2+30x=0\\ \Rightarrow x\left(x^2-11x+30\right)=0\end{array}$

One root will be 0.

Descartes rule of signs shows there are 2 or 0 positive roots and since:

  ${\left(-x\right)}^2-11\left(-x\right)+30=x^2+11x+30$

There are no negative roots.

  $x\left(x-6\right)\left(x-5\right)=0$

  $x=0,5,6$