Chapter 4.6, Problem 50E

(a)

To determine

To find: the number of positive real zeros does the function have negative real zeros and imaginary zeros.

Answer to Problem 50E

The function has two positive real roots and one negative real root.

There will be three imaginary roots.

Explanation of Solution

Given information:

The graph represents a polynomial function of degree 6.

  

Calculation:

From the graph it is very clear that function touches positive $x$ axis at one point and crosses negative $x$ axis at one point. So, the function has two positive real roots and one negative real root.

Because degree of function is 6, so there will be three imaginary roots.

(b)

To determine

To describe: the possible sign changes in the coefficients of $f\left(x\right)$ using Descarte’s rule of signs.

Explanation of Solution

Given information:

The graph represents a polynomial function of degree 6.

  

Calculation:

Because the function has two positive real roots and one negative real roots, so possible sign change in coefficient of $f\left(x\right)$ is 4.