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Chapter 6: Q26. (page 298)

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

14x+x2+49=0

Short Answer

Expert verified

The solution to the equation 14x+x2+49=0is x=-7.

Step by step solution

01

Step 1. Given Information.

Given to solve the equation 14x+x2+49=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 at -7.

Hence the solution to the equation 14x+x2+49=0is x=-7.

03

Step 3. Conclusion.

Therefore, the solution to the equation 14x+x2+49=0is x=-7

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Most popular questions from this chapter

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=x2+4

An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by h(t)=-16t2+80t+200. Interpret the meaning of the y-intercept in the context of this problem.

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

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

f(x)=3-x2-6x

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=x2-23x-89
See all solutions

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