Chapter 4: Q. 26 (page 215)

use the given zero to find the remaining zeros of each function.
$h (x) = 3 x^{4} + 5 x^{3} + 25 x^{2} + 45 x - 18; z e r o : 3 i$

Short Answer

Expert verified

The roots of the polynomial are $3 i, - 3 i, - 2, \frac{1}{3}$

Step by step solution

Given information

We are given a polynomial $h (x) = 3 x^{4} + 5 x^{3} + 25 x^{2} + 45 x - 1$

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,

$3 i 3 5 25 45 - 18 9 i 15 i - 27 - 45 i - 6 i 18 3 5 + 9 i 15 i - 2 - 6 i 0$

Now we use -3i in the synthetic division

role="math" localid="1647482204687" $- 3 i 3 5 + 9 i 15 i - 2 - 6 i - 9 i - 15 i 6 i 3 5 - 2 0$

Hence we have,

$h (x) = (x - 3 i) (x + 3 i) (3 x^{2} + 5 x - 2)$

Use factorization to find the remaining roots

$3 x^{2} + 5 x - 2 = 0 (3 x - 1) (x + 2) = 0 x = \frac{1}{3} o r x = - 2$

Conclusion

The roots of the polynomial are $3 i, - 3 i, \frac{1}{3}, - 2$

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use the given zero to find the remaining zeros of each function.
$h (x) = 3 x^{4} + 5 x^{3} + 25 x^{2} + 45 x - 18; z e r o : 3 i$

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

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

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

use the given zero to find the remaining zeros of each function.
$h (x) = 3 x^{4} + 5 x^{3} + 25 x^{2} + 45 x - 18; z e r o : 3 i$