College Algebra (10th Edition)

Published by Pearson

Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding - Page 387: 24

Answer

The maximum number of real zeros is $5$ The number of positive real zeros is $1$ The number of negative real zeros is $0$

Work Step by Step

Number of zeros of a polinomial can’t be greater than its degree $1)$ Number of positive real zeros of $f(x)$ either equals the number of variations in the sign of the nonzero coefficients of $f(x)$ or equals that number minus an even integer $2)$ Number of negative real zeros of $f(x)$ either equals the number of variations in the sign of the nonzero coefficients of $f(-x)$ or equals that number minus an even integer. So the maximum number of real zero here is $5$ Since $$f\left( x\right) =-3x^{5}+4x^{4}+2$$ has $1$ variation The number of positive real zero is $1$ Since $$f\left( -x\right) =3x^{5}+4x^{4}+2$$ Has $0$ variations The number of negative real zeros is $0$

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