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Chapter 4: Q. 34 (page 215)

find the complex zeros of each polynomial function. Write f in factored form

f(x)=x3+13x2+57x+85

Short Answer

Expert verified

The complex roots of the polynomial are 4+i and 4-i

Step by step solution

01

Given information

We are given a polynomialf(x)=x3+13x2+57x+85

02

Find the factors

To find the factors of the polynomial we first have to find the factors of 85,

They can be given as卤1,卤5,卤17,卤85

Let us try -5 using synthetic division

role="math" localid="1647572985088" -51135785-5-40-8518170

hence the polynomial becomes

role="math" localid="1647573001820" f(x)=(x+5)(x2+8x+17)Nowweusequadraticformulatofindtheremainingfactorsx=-8卤64-682x=-8卤2i2x=4卤i

03

Conclusion

The complex roots of the polynomial are 4+i and 4-i

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Most popular questions from this chapter

Find the domain of the rational function.

-4x2x-2(x+4)

Solve the inequality algebraically

x3-2x2-3x>0

Find the real zeros of f. Use the real zeros to factor f.

x3+8x2+11x-20

Graph each rational function using transformations.

R(x)=1x-1+1

Solve the given inequality algebraically.

x3>1
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