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Chapter 4: Q. 27 (page 215)

use the given zero to find the remaining zeros of each function.

h(x)=x4-9x3+21x2+21x-130;zero:3-2i

Short Answer

Expert verified

The roots of the polynomial are3+2i,3-2i,5,-2

Step by step solution

01

Given information

We are given a polynomialh(x)=x4-9x3+21x2+21x-130

02

Find the roots using synthetic division

As 3+2i is a root of the polynomial by conjugate properties 3-2i is also a root of the polynomial

Hence

3-2i1-92121-1303-2i-22+6i9+20i1301-6-2i-1+6i30+20i0

Now we use 3+2i in synthetic division

3+2i1-6-2i-1+6i30+20i3+2i-9-6i-30-20i1-3-100

Hence we have,

h(x)=(x-(3-2i))(x-(3+2i))(x2-3x-10)

Now we use facotring to find the remaining roots

x2-3x-10=0(x-5)(x+2)=0x=5orx=-2

03

Conclusion

The roots of the polynomial are3-2i,3+2i,5,-2

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Most popular questions from this chapter

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