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Chapter 6: Q32. (page 298)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

x2+3x-2=0

Short Answer

Expert verified

The solutions to the equation x2+3x-2=0 lie between-4 and -3, 0and 1.

Step by step solution

01

Step 1. Given Information.

Given to solve the equation x2+3x-2=0 by graphing. And if the exact roots cannot be found, the consecutive integers between which the roots are located are to be determined.

02

Step 2. Explanation.

A quadratic equation has a real solution where the graph of the related function crosses or touches the x-axis.

Graphing the given equation using graphing calculator:

From the given graph, the function crosses the x axis between -4 and -3 and then in between 0 and 1.

Hence the solutions to the equation x2+3x-2=0 lie between -4 and -3, 0 and 1.

03

Step 3. Conclusion.

Therefore, the solutions to the equation x2+3x-2=0 lie between -4 and -3, 0 and 1.

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Most popular questions from this chapter

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=4x-x2+1

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

2x2-2x-3=0

The shape of each arch supporting the Exchange House can be modeled by h(x)=-0.025x2+2x, where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base in meters.

According to this model, what is the maximum height of the arch?

State whether the graph of each quadratic function opens up or down. Then state whether the function has a maximum or minimum value.

a.f(x)=3x2+4x−5b.f(x)=−2x2+9c.f(x)=−5x2−8x+2d.f(x)=6x2−5x

Complete parts a-c for each quadratic function.

a. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.

b. Make a table of values that includes the vertex.

c. Use this information to graph the function.

f(x)=-0.25x2-3x
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