Chapter 4: Q. 28 (page 215)

use the given zero to find the remaining zeros of each function.
$f (x) = x^{4} - 7 x^{3} + 14 x^{2} - 38 x - 60; z e r o : 1 + 3 i$

Short Answer

Expert verified

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

Step by step solution

Given information

We are given a polynomial $f (x) = x^{4} - 7 x^{3} + 14 x^{2} - 38 x - 60$

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

$1 + 3 i 1 - 7 14 - 38 - 60 1 - 3 i - 15 + 15 i 44 + 18 i 60 1 - 6 - 3 i - 1 + 15 i 6 + 18 i 0$

Now we use 1-3i in synthetic divsion

$1 + 3 i 1 - 6 - 3 i - 1 + 15 i 6 + 18 i 1 + 3 i - 5 - 15 i - 6 - 18 i 1 - 5 - 6 0$

hence we get,

$f (x) = (x - (1 + 3 i) (x - (1 - 3 i)) (x^{2} - 5 x - 6)$

Now we use factoring to find the remaining roots

$x^{2} - 5 x - 6 = 0 (x - 6) (x + 1) = 0 x = 6 o r x = - 1$

Conclusion

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

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use the given zero to find the remaining zeros of each function.
$f (x) = x^{4} - 7 x^{3} + 14 x^{2} - 38 x - 60; z e r o : 1 + 3 i$

Short Answer

Step by step solution

Given information

Find the roots of the polynomial using synthetic division

Conclusion

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use the given zero to find the remaining zeros of each function.f(x)=x4-7x3+14x2-38x-60;zero:1+3i

Short Answer

Step by step solution

Given information

Find the roots of the polynomial using synthetic division

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Probability and Statistics

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

use the given zero to find the remaining zeros of each function.
$f (x) = x^{4} - 7 x^{3} + 14 x^{2} - 38 x - 60; z e r o : 1 + 3 i$