Chapter 4: Q. 27 (page 215)

use the given zero to find the remaining zeros of each function.
$h (x) = x^{4} - 9 x^{3} + 21 x^{2} + 21 x - 130; z e r o : 3 - 2 i$

Short Answer

Expert verified

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

Step by step solution

Given information

We are given a polynomial $h (x) = x^{4} - 9 x^{3} + 21 x^{2} + 21 x - 130$

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

$3 - 2 i 1 - 9 21 21 - 130 3 - 2 i - 22 + 6 i 9 + 20 i 130 1 - 6 - 2 i - 1 + 6 i 30 + 20 i 0$

Now we use 3+2i in synthetic division

$3 + 2 i 1 - 6 - 2 i - 1 + 6 i 30 + 20 i 3 + 2 i - 9 - 6 i - 30 - 20 i 1 - 3 - 10 0$

Hence we have,

$h (x) = (x - (3 - 2 i)) (x - (3 + 2 i)) (x^{2} - 3 x - 10)$

Now we use facotring to find the remaining roots

$x^{2} - 3 x - 10 = 0 (x - 5) (x + 2) = 0 x = 5 o r x = - 2$

Conclusion

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

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use the given zero to find the remaining zeros of each function.
$h (x) = x^{4} - 9 x^{3} + 21 x^{2} + 21 x - 130; z e r o : 3 - 2 i$

Short Answer

Step by step solution

Given information

Find the roots using synthetic division

Conclusion

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use the given zero to find the remaining zeros of each function.h(x)=x4-9x3+21x2+21x-130;zero:3-2i

Short Answer

Step by step solution

Given information

Find the roots using synthetic division

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Geometry

Mechanics Maths

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

use the given zero to find the remaining zeros of each function.
$h (x) = x^{4} - 9 x^{3} + 21 x^{2} + 21 x - 130; z e r o : 3 - 2 i$