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Consider the function f(x) = 2x* - x' +7x2 -4x-4 whose graph is pictured below. What do you notice about this graph that does not make sense based on the degree of the function? What conclusion can you draw about the four roots of the function, (x)? Explain your reasoning.

Consider the function f(x) = 2x* - x' +7x2 -4x-4 whose graph is pictured below. What do you notice about this graph that does not make sense based on the degree of the function? What conclusion can you draw about the four roots of the function, (x)? Explain your reasoning.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the function f(x) = 2x* –x' + 7x2 – 4x – 4 whose graph is pictured below. What do you notice about this graph that does not make sense based on the degree of the function? What conclusion can you draw about the four roots of the function, (x)? Explain your reasoning. Make a list of the rational roots that the Rational Root Theorem guarantees are possible. From this list, which roots appear to be roots from the graph above? Perform synthetic division to verify that they are, in fact, roots. Divide f(x) by one of the associated factors. Then, divide that result by the other associated factor. You have just divided a degree 4 function twice so your resulting polynomial is a This function's roots will be the remaining two roots, which will be imaginary, of f(x). Find these imaginary roots.
Transcribed Image Text:Consider the function f(x) = 2x* –x' + 7x2 – 4x – 4 whose graph is pictured below. What do you notice about this graph that does not make sense based on the degree of the function? What conclusion can you draw about the four roots of the function, (x)? Explain your reasoning. Make a list of the rational roots that the Rational Root Theorem guarantees are possible. From this list, which roots appear to be roots from the graph above? Perform synthetic division to verify that they are, in fact, roots. Divide f(x) by one of the associated factors. Then, divide that result by the other associated factor. You have just divided a degree 4 function twice so your resulting polynomial is a This function's roots will be the remaining two roots, which will be imaginary, of f(x). Find these imaginary roots.
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