Chapter 5.7, Problem 49PPS

a.

To determine

To find the number of positive real zeros, negative real zeros and imaginary zeros.

Answer to Problem 49PPS

The polynomial has $\text{2}$ positive real zeros, $1$ negative real zero and $3$ imaginary zeros.

Explanation of Solution

Given:

The given function is:

  $P(x)=-0.006x^4+0.15x^3-0.05x^2-1.8x$

Calculation:

The number of positive real zeros, negative real zeros and imaginary zeros are determined as follows:

Consider the function;

  $P(x)=-0.006x^4+0.15x^3-0.05x^2-1.8x$

There are $2$ sign changes for the coefficients of $p(x)$ , hence the function has $0\text{ or 2}$ positive real zeros.

  $P(-x)=-0.006x^4-0.15x^3-0.05x^2+1.8x$

There are $1$ sign changes for the coefficients of $p(-x)$ , so $p(x)$ has $1$ negative real zeros.

Hence, $p(x)$ has $\text{ 2}$ positive real zeros, $1$ negative real zero and $3$ imaginary zeros.

b.

To determine

To explain the meaning of zeros for this situation.

Explanation of Solution

The negative zero won’t be suitable for this situation, because, the number of computer produced can’t be negative. Since, the zeros are value of $x$ , then $p(x)=0$ is non-negative zeros represents numbers of computers produced per hour will lead to no profit to the owner.