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Chapter 4: Q. 33 (page 215)

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

f(x)=x3-8x2+25x-26

Short Answer

Expert verified

The complex roots of the polynomial are 3+2i, 3-2i

Step by step solution

01

Given information

We are given a polynomialf(x)=x3-8x2+25x-26

02

Find the factors

To find the factors of the polynomial we first find the factors of -26

They can be given as 卤1,卤2,卤13,卤26

Let us test 2 using synthetic division whether we get zero or not

21-825-262-12261-6130

Hence the polynomial can be given as

f(x)=(x-2)(x2-6x+13)

Now using quadratic formula find the remaining factors

x2-6x+13=0x=-b卤b2-4ac2ax=6卤36-522x=6卤4i2x=3卤2i

03

Conclusion

The complex roots of the polynomial are 3+2i, 3-2i

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Most popular questions from this chapter

Graph each rational function using transformations.

F(x)=2-1x+1

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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.

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