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Factor the polynomial and use the factored form to find the real zeros. (Enter your answers as a comma-separated list. Enter all answers including repetition P(x) = x4 - 3x2 - 4 0,2,-2, 1i, - li X= Sketch the graph. X 10 5 -10 5 X -5 -5 -10 5 X

Factor the polynomial and use the factored form to find the real zeros. (Enter your answers as a comma-separated list. Enter all answers including repetition P(x) = x4 - 3x2 - 4 0,2,-2, 1i, - li X= Sketch the graph. X 10 5 -10 5 X -5 -5 -10 5 X

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Polynomial Factoring and Graphing** **Task Description:** - **Problem Statement:** Factor the polynomial and use the factored form to find the real zeros. Then, sketch the graph of the polynomial. - **Given Polynomial:** \[ P(x) = x^4 - 3x^2 - 4 \] - **Provided Roots:** \[ x = 0, 2, 2, 1i, -1i \] (Note: The red "X" indicates that this is an incorrect list of zeros.) **Graph Explanation:** - **Graph Overview:** The polynomial graph displays two separate sections, both illustrating a typical parabolic curve. - **Axes:** - Both graphs are plotted with the x-axis and y-axis ranging approximately from -5 to 5. - The y-axis ranges from -10 to 10, providing a view of the graph's symmetry and end behaviors. - **Graph Details:** - **Intersection Points:** The graph intersects the x-axis at certain points, which are potential real zeros. The precise zeros are not clear in the incorrect list provided. - **Curve Behavior:** The curve appears to have a central dip between the y-values of -5 and -10, indicating potential minima or maxima. - **Visual Representation:** - The blue curve on each graph section is reflective of typical quartic polynomial behavior, where the ends go off towards positive infinity, suggesting a general U-shape with a dip. **Note:** The correct factorization and identification of real zeros should be verified since the list provided has been marked incorrect. Accurate solutions will adjust the graph interpretation accordingly.
Transcribed Image Text:**Polynomial Factoring and Graphing** **Task Description:** - **Problem Statement:** Factor the polynomial and use the factored form to find the real zeros. Then, sketch the graph of the polynomial. - **Given Polynomial:** \[ P(x) = x^4 - 3x^2 - 4 \] - **Provided Roots:** \[ x = 0, 2, 2, 1i, -1i \] (Note: The red "X" indicates that this is an incorrect list of zeros.) **Graph Explanation:** - **Graph Overview:** The polynomial graph displays two separate sections, both illustrating a typical parabolic curve. - **Axes:** - Both graphs are plotted with the x-axis and y-axis ranging approximately from -5 to 5. - The y-axis ranges from -10 to 10, providing a view of the graph's symmetry and end behaviors. - **Graph Details:** - **Intersection Points:** The graph intersects the x-axis at certain points, which are potential real zeros. The precise zeros are not clear in the incorrect list provided. - **Curve Behavior:** The curve appears to have a central dip between the y-values of -5 and -10, indicating potential minima or maxima. - **Visual Representation:** - The blue curve on each graph section is reflective of typical quartic polynomial behavior, where the ends go off towards positive infinity, suggesting a general U-shape with a dip. **Note:** The correct factorization and identification of real zeros should be verified since the list provided has been marked incorrect. Accurate solutions will adjust the graph interpretation accordingly.
Expert Solution
Step 1

Here we have given a polynomialp(x)=x4-3x2-4.

Now let x2=t

⇒p(t)=t2-3t-4

Now using the Quadratic formula to find the value of 't' we get:
⇒t=-(-3)±(-3)2-4(1)(-4)2(1)⇒t=3±9+162=3±252⇒t=3±52

⇒t=3+52=4 and t=3-52=-1

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