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Chapter 4: Q. 37 (page 215)

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

f(x)=x4+2x3+22x2+50x-75

Short Answer

Expert verified

The complex roots of the polynomial is5i,-5i

Step by step solution

01

Given information

We are given a polynomialf(x)=x4+2x3+22x2+50x-75

02

Factor the polynomial

We get,

x4+2x3+22x2+50x-75=0x4+2x3-3x2+25x2+50x-75=0x2(x2+2x-3)+25(x2+2x-3)=0(x2+25)(x2+2x-3)=0(x-5i)(x+5i)(x+3)(x-1)=0

03

Conclusion

The complex roots of the polynomial are5i,-5i

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Most popular questions from this chapter

In Problems 57鈥� 62, find the real zeros of f. If necessary, round to two decimal places.

f(x)=x3+42.2x2-664.8x+1490.4

In Problems 13鈥�24, find the domain of each rational function.

R(x)=3(x2-x-6)4(x2-9)

True or False. If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients give rise to the horizontal asymptote.

True or False : A test number for the interval-2<x<5could be 4.

For a rational functionR, if the degree of the numerator is less than the degree of the denominator, then R is ________.
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