Chapter 4.6, Problem 5E

To determine

To identify: the number of solutions or zeros.

Answer to Problem 5E

The equation has 3 solutions.

Explanation of Solution

Given information:

Given equation,

  $9t^6-14t^3+4t-1=0$

Calculation:

Consider the equation $9t^6-14t^3+4t-1=0$ :

The fundamental theorem of algebra states that “if $f\left(x\right)$ is a degree of polynomial $n$ where $n>0$ , then the equation $f\left(x\right)=0$ has exactly $n$ solution”.

The degree of polynomial equation $9t^6-14t^3+4t-1=0$ is 6.

Therefore, the equation has 6 solutions.