Explanation Given information: The equation is x 4 − 5 x 2 + 4 = 0 and the viewing rectangle is [ − 4 , 4 ] by [ − 30 , 30 ] . Concept used: Rational zeroes theorem: If the polynomial P ( x ) = a n x n + a n − 1 x n − 1 + a n − 2 x n − 2 + .... + a 2 x + a 1 x + a 0 has integer coefficients, here a n ≠ 0 and a 0 ≠ 0 , then the all rational roots of the polynomial P ( x ) is in the form of p q . Here, p and q are integers and p is a factor of the constant coefficient a 0 and q is a factor of the leading coefficient a n . Calculation: The given equation is x 4 − 5 x 2 + 4 = 0 . The leading coefficient is 1 and the constant coefficient is 4 . By the Rational Zeros Theorem, the rational zeros of polynomial P ( x ) are the ratio of the factors of 4 to the factors of 1. The factors of the constant coefficient 4 are ± 1 , ± 2 , ± 4 and the factors of the leading coefficient 1 are ± 1 . Therefore, the values of p are ± 1 , ± 2 , ± 4 and the values of q are ± 1 . Thus, all possible rational roots are ± 1 , ± 2 , ± 4 . Graph: To graph the equation x 4 − 5 x 2 + 4 = 0 first turn on the calculator, then press the WINDOW button and set the viewing window or viewing rectangle as shown below in Figure 1. Figure 1 Now press the button Y = and insert the equation as shown below in Figure 2. Figure 2 After this press the GRAPH button and the graph is obtained as shown in Figure 3. Figure 3 Now proceed with the above graph and to obtain the solutions, press 2 n d and TRACE simultaneously and then select INTERSECT to obtain the intersection point between two curves. Now press ENTER to obtain the first intersection point of the equation x 4 − 5 x 2 + 4 = 0 as shown below in Figure 4.

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 3.4, Problem 92E

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All possible rational roots of the equation x4−5x2+4=0 using Rational zeroes theorem, and then graph the polynomial in the given viewing rectangle [−4,4] by [−30,30].

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Chapter 3.4, Problem 91E

Chapter 3.4, Problem 93E

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All possible rational roots of the equation x 4 − 5 x 2 + 4 = 0 using Rational zeroes theorem, and then graph the polynomial in the given viewing rectangle [ − 4 , 4 ] by [ − 30 , 30 ] .

Solution Summary: The author calculates the rational roots of the polynomial P(x) using the Rational Zeroes Theorem.

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To find:

All possible rational roots of the equation x4−5x2+4=0 using Rational zeroes theorem, and then graph the polynomial in the given viewing rectangle [−4,4] by [−30,30].

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Chapter 3 Solutions

All possible rational roots of the equation x 4 − 5 x 2 + 4 = 0 using Rational zeroes theorem, and then graph the polynomial in the given viewing rectangle [ − 4 , 4 ] by [ − 30 , 30 ] .

Solution Summary: The author calculates the rational roots of the polynomial P(x) using the Rational Zeroes Theorem.

Concept explainers

Videos

To find: All possible rational roots of the equation x4−5x2+4=0 using Rational zeroes theorem, and then graph the polynomial in the given viewing rectangle [−4,4] by [−30,30].

Want to see the full answer?

Chapter 3 Solutions

To find:

All possible rational roots of the equation x4−5x2+4=0 using Rational zeroes theorem, and then graph the polynomial in the given viewing rectangle [−4,4] by [−30,30].