Explanation Approach: Solve the polynomial equation f ( x ) = 0 to get the zeros of the polynomial function. If a is a zero with an odd multiplicity, the graph crosses the x -axis at x = a . If a is a zero with an even multiplicity, the graph touches the x -axis and turns at x = a . Calculation: Given: f ( x ) = x 4 − 4 x 3 + 3 x 2 We will set the polynomial function f ( x ) equal to 0 and solve the polynomial equation to get the zeros of the polynomial function. Substitute f ( x ) = 0 in the equation f ( x ) = x 4 − 4 x 3 + 3 x 2 . f ( x ) = x 4 − 4 x 3 + 3 x 2 0 = x 4 − 4 x 3 + 3 x 2 Factor out x 2 from the all terms, = x 4 − 4 x 3 + 3 x 2 = x 2 ( x 2 − 4 x + 3 ) Factorize x 2 − 4 x + 3 as ( x − 3 ) ( x − 1 ) = x 2 ( x − 3 ) ( x − 1 ) By the zero factor property, x 2 = 0 x = 0 (twice) x − 3 = 0 x − 1 = 0 Taking, x − 3 = 0 Add 3 on both sides, x − 3 + 3 = 0 + 3 x = 3 Taking, x − 1 = 0 Add 1 on both sides, x − 1 + 1 = 0 + 1 x = 1 Thus, zero of the polynomial function are x = 3 , x = 1 and x = 0

WebAssign with Corequisite Support for Gustafson/Hughes' College Algebra, 12th Edition [Instant Access], Single-Term

12th Edition

ISBN: 9780357422533

Author: Gustafson; R. David; Hughes; Jeff

Publisher: Cengage Learning US

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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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Chapter 4.CR, Problem 19E

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The zeros with their multiplicity of the polynomial function f(x)=x4−4x3+3x2 and state whether the graph touches the x-axis and turns or crosses the x-axis at the zeros.

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Chapter 4.CR, Problem 18E

Chapter 4.CR, Problem 20E

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WebAssign with Corequisite Support for Gustafson/Hughes' College Algebra, 12th Edition [Instant Access], Single-Term

Ch. 4.1 - Find the vertex of the graph of the quadratic...Ch. 4.1 - Prob. 2SC Ch. 4.1 - Prob. 3SC Ch. 4.1 - Prob. 4SC Ch. 4.1 - Find the largest area possible if the association...Ch. 4.1 - A company that makes and sells baseball caps has...Ch. 4.1 - Fill in the blanks. A quadratic function is...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E

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The zeros with their multiplicity of the polynomial function f ( x ) = x 4 − 4 x 3 + 3 x 2 and state whether the graph touches the x -axis and turns or crosses the x -axis at the zeros.

Solution Summary: The author explains how to find the zeros with their multiplicity of the polynomial function f(x)=0 and state whether the graph touches the x -axis and turns

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To find:

The zeros with their multiplicity of the polynomial function f(x)=x4−4x3+3x2 and state whether the graph touches the x-axis and turns or crosses the x-axis at the zeros.

Want to see the full answer?

Chapter 4 Solutions

The zeros with their multiplicity of the polynomial function f ( x ) = x 4 − 4 x 3 + 3 x 2 and state whether the graph touches the x -axis and turns or crosses the x -axis at the zeros.

Solution Summary: The author explains how to find the zeros with their multiplicity of the polynomial function f(x)=0 and state whether the graph touches the x -axis and turns

Concept explainers

Videos

To find: The zeros with their multiplicity of the polynomial function f(x)=x4−4x3+3x2 and state whether the graph touches the x-axis and turns or crosses the x-axis at the zeros.

Want to see the full answer?

Chapter 4 Solutions

To find:

The zeros with their multiplicity of the polynomial function f(x)=x4−4x3+3x2 and state whether the graph touches the x-axis and turns or crosses the x-axis at the zeros.