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We need to find all the zeros (real & complex) of the polynomial function f(x) = x6 – 64. (a) Write f(x) as a product of two cubic functions fi (x) and f2(x). (b) Work out all the zeros (real & complex) of fi(x). (c) Work out all the zeros (real & complex) of f2(x). (d) Convince yourself that the zeros of f(x) form a set which is the union of the sets of zeros of fi(x) and f2(x). (e) Use synthetic division to verify that the zeros obtained in (d) are indeed true.

We need to find all the zeros (real & complex) of the polynomial function f(x) = x6 – 64. (a) Write f(x) as a product of two cubic functions fi (x) and f2(x). (b) Work out all the zeros (real & complex) of fi(x). (c) Work out all the zeros (real & complex) of f2(x). (d) Convince yourself that the zeros of f(x) form a set which is the union of the sets of zeros of fi(x) and f2(x). (e) Use synthetic division to verify that the zeros obtained in (d) are indeed true.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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We need to find all the zeros (real & complex) of the polynomial function f(x) = x6 – 64. (a) Write f(x) as a product of two cubic functions fi (x) and f2(x). (b) Work out all the zeros (real & complex) of fi(x). (c) Work out all the zeros (real & complex) of f2(x). (d) Convince yourself that the zeros of f(x) form a set which is the union of the sets of zeros of f,(x) and f2(x). (e) Use synthetic division to verify that the zeros obtained in (d) are indeed true.
Transcribed Image Text:We need to find all the zeros (real & complex) of the polynomial function f(x) = x6 – 64. (a) Write f(x) as a product of two cubic functions fi (x) and f2(x). (b) Work out all the zeros (real & complex) of fi(x). (c) Work out all the zeros (real & complex) of f2(x). (d) Convince yourself that the zeros of f(x) form a set which is the union of the sets of zeros of f,(x) and f2(x). (e) Use synthetic division to verify that the zeros obtained in (d) are indeed true.
Question 1: Show that the distance x in the figure is a solution of the equa- tion x* - 16x + 500x² – 8000x + 32,000 = 0 and find the value of D by following these steps. 30 y 20 8 D-и и -D- (a) Use the similar triangles in the diagram and the properties of proportions learned in geometry to show that 8 у - 8 y 8x (b) Show that y х — 8° (c) Show that y2 - x2 plify to obtain the desired degree 4 equation in x. = 500. Then substitute for y, and sim- (d) Find the distance D.
Transcribed Image Text:Question 1: Show that the distance x in the figure is a solution of the equa- tion x* - 16x + 500x² – 8000x + 32,000 = 0 and find the value of D by following these steps. 30 y 20 8 D-и и -D- (a) Use the similar triangles in the diagram and the properties of proportions learned in geometry to show that 8 у - 8 y 8x (b) Show that y х — 8° (c) Show that y2 - x2 plify to obtain the desired degree 4 equation in x. = 500. Then substitute for y, and sim- (d) Find the distance D.
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