EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form o…
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Chapter 2.5, Problem 119E
To determine

To describe:The errorin the equation of f(x)=(x+2)(x−3.5)(x−i) .

Expert Solution & Answer
Check Mark

Answer to Problem 119E

  f(x)=(x+2)(x−3.5)(x−i)(x+i)

Explanation of Solution

Given:

The function y=f(x) is a quartic polynomial. One of its zeros is i . And the graph of the function is given below:

  EBK PRECALCULUS W/LIMITS, Chapter 2.5, Problem 119E

Concept Used:

Factor theorem:

“For a polynomial P(x) , r is a zero of a polynomial if and only if x−r is a factor of P(x) ”.

Since, one of its zeros is i which is a complex number and it is known that complex zeros always exist as conjugate pairs. So, its another zero is −i .

Also, on observing the graph it can be noticed that the graph intersects the x -axis at x=−2 and x=3.5 . So, x=−2 and x=3.5 are also a zero of this function.

So, by factor theorem, (x+2) , (x−3.5) , (x−(1+i)) and (x−(1−i)) are the factors of given function.

And since it’s a quarticpolynomial it can have at most 4 linear factors.

  f(x)=(x+2)(x−3.5)(x−i)(x+i)

Conclusion:

The correctequation of f(x) is f(x)=(x+2)(x−3.5)(x−i)(x+i) .

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Chapter 2.5, Problem 118E
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Chapter 2.5, Problem 120E

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

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10 - Roots of polynomials; Author: Technion;https://www.youtube.com/watch?v=88YUeigknNg;License: Standard YouTube License, CC-BY