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Chapter 4: Q. 30 (page 242)

Solve the inequality algebraically.

x4<9x2

Short Answer

Expert verified

The required interval set is :

(-3,3)

Step by step solution

01

Step 1. Given inequality 

x4<9x2

we need to solve for x.

02

Step 2. Factorization

x4-9x2<0x2(x2-9)<0x2(x+3)(x-3)<0

The zeros of the given equation are :

0,3,-3localid="1646130204622" 0,3,-3

03

Step 3. Dividing the number line into 3 intervals 

(-鈭�,-3)(-3,3)(3,鈭�)

04

Step 4. Evaluating the value of function at different intervals

3. (-鈭�,-3)

let us take the value -4

the value of function at -4

=112

2.(-3,3)

let us take the number 2

the value of the function at x=2 is :

=-20

1. (3,鈭�)

let us take the value 4

the value of function at x= 4

=112

05

Step 5. Conclusion

The required interval set is :

(-3,3)

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Most popular questions from this chapter

In Problems 63鈥�72, find the real solutions of each equation.

3x3+4x2-7x+2=0

In Problems 39鈥�56, find the real zeros of f. Use the real zeros to factor f.

f(x)=4x5-8x4-x+2

In Problems 21鈥�32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=-4x3-x2+x+2

In Problems 49鈥� 60, for each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.

(c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of |x|

f(x)=3(x-7)(x+3)2

Write a few paragraphs that provide a general strategy for graphing a polynomial function. Be sure to mention the following: degree, intercepts, end behavior, and turning points.
See all solutions

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