Chapter 4.4, Problem 16E

To determine

To state: The number of complex roots, the number of positive real roots and the number of negative real roots of $x^4-2x^3+7x^2+4x-15=0$ .

Answer to Problem 16E

There are 2 complex roots

Explanation of Solution

Given information: $x^4-2x^3+7x^2+4x-15=0$

Calculation:

  $x^4-2x^3+7x^2+4x-15=0$

By Descartes Rule of signs:

1 or 3 positive rational roots

1 negative rational root

Possible zeros: $\pm 1\text{, }\pm \text{3, }\pm \text{5, }\pm \text{15}$

  

Graph shows none of these are on the graph. This means none of the roots are “rational”.

You can see 2 zeros on the graph, 1 positive irrational roots and 1 negative irrational root.

This means there are 2 complex roots.