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Chapter 4: Q. 26 (page 215)

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

h(x)=3x4+5x3+25x2+45x-18;zero:3i

Short Answer

Expert verified

The roots of the polynomial are3i,-3i,-2,13

Step by step solution

01

Given information

We are given a polynomialh(x)=3x4+5x3+25x2+45x-1

02

Find the roots using synthetic division

As 3i is one the roots of the polynomial by conjugate pairs property -3i is also a root of the polynomial

We use synthetic division to find the remaining roots of the polynomial

Hence,

3i352545-189i15i-27-45i-6i1835+9i15i-2-6i0

Now we use -3i in the synthetic division

role="math" localid="1647482204687" -3i35+9i15i-2-6i-9i-15i6i35-20

Hence we have,

h(x)=(x-3i)(x+3i)(3x2+5x-2)

Use factorization to find the remaining roots

3x2+5x-2=0(3x-1)(x+2)=0x=13orx=-2

03

Conclusion

The roots of the polynomial are3i,-3i,13,-2

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Most popular questions from this chapter

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

Solve the inequality algebraically.

x4>x2

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)=x5-x4+2x2+3

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

f(x)=x3-8x2+17x-6

Analyze each polynomial function using Steps 1through 8:

f(x)=x4+x3-3x2-x+2.
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