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Chapter 4: Q. 28 (page 215)

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

f(x)=x4-7x3+14x2-38x-60;zero:1+3i

Short Answer

Expert verified

The roots of the polynomial are1+3i,1-3i,6,-1

Step by step solution

01

Given information

We are given a polynomialf(x)=x4-7x3+14x2-38x-60

02

Find the roots of the polynomial using synthetic division

We have 1+3i as one root of the polynomial hence by conjugate properties 1-3i is also a root of the polynomial

hence

1+3i1-714-38-601-3i-15+15i44+18i601-6-3i-1+15i6+18i0

Now we use 1-3i in synthetic divsion

1+3i1-6-3i-1+15i6+18i1+3i-5-15i-6-18i1-5-60

hence we get,

f(x)=(x-(1+3i)(x-(1-3i))(x2-5x-6)

Now we use factoring to find the remaining roots

x2-5x-6=0(x-6)(x+1)=0x=6orx=-1

03

Conclusion

The roots of the polynomial are1+3i,1-3i,6,-1

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