Chapter 4, Problem 11STP

(a)

To determine

To find: The number of real roots that the quadratic function have.

Answer to Problem 11STP

The number of real roots are zero.

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

From the graph shown in Figure 1 it is clear that there are no real roots of the function as the graph of the function lies in the negative x-axis.

(b)

To determine

To find: The number of complex roots that the quadratic function have.

Answer to Problem 11STP

The number of complex roots are two.

Explanation of Solution

From the graph shown in Figure 1, the number of complex roots are two.

(c)

To determine

To find: The discriminant of the quadratic equation.

Answer to Problem 11STP

The number of complex roots are 2 so the discriminant is less than 0.

Explanation of Solution

The discriminant of the quadratic equation is of the form,

  $b^2-4ac<0$

The number of complex roots are 2 so the discriminant is less than 0.