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Assignment3C
Aftercompletinglesson3C,completetheassignmentbelow.
Simplifythefollowingexpressions.
Simplifythefollowingexpressions.
1. 3 3. $ + $ − 5. & + '& − '
2. 2 + 31 − 4
4. $ − √3$ + √3
6. Complexconjugatesaretwocomplexnumbersoftheform& + 'and& − '.
Whathappenseverytimeyoumultiplytwocomplexconjugatesasinproblems3-5?
7. Considerapolynomial0$ = $ 2 + $ 3 − 4$ + 2$ − 12thatcanbewrittenwithalinear
factorizationoftheform0$ = $ − 5$ − 6$ − 7$ − 8.
Iftwoofthesefactorcontaincomplexnumbers,explainwhydoweknowthattwoofthe
termsmustbecomplexconjugates?Hint:Consideryouranswerto#6
8. Thepolynomial0$ = $ 2 + $ 3 − 4$ + 2$ − 12haszerosat$ = −3and$ = 2.
a. Findarealfactorizationof0$.
b. Findthecomplexzerosof0$.
c. Writethelinearfactorizationwithrealandcomplexfactorsof0$.
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9. StatetheFundamentalTheoremofAlgebra.
10. Considerthequartic4thdegreefunctiongraphedtotheright.
a. Howmanyrealzerosdoesthefunctionhave?Explain.
b. Doesthefunctionhaveanycomplexzeros?Ifso,howmany?
Explainhowyouknow.
11. Foreachquarticfunctionbelow,statehowmanyrealzerosincludingrepeatedzerosand
howmanyimaginaryzerosithas.
a b c Completelyfactorthepolynomials.Youmayuseyourcalculatortostart,syntheticdivision,
Completelyfactorthepolynomials.Youmayuseyourcalculatortostart,syntheticdivision,
factoring,orthequadraticformula.Leaveanswersasexactanswersin
factoring,orthequadraticformula.Leaveanswersasexactanswersin
simplifiedform.
sinsimplifiedform.
orm.
2
3
12. $ + 2$ + $ + 8$ − 12
13. $ 2 − 2$ 3 − 6$ − 7$ − 4
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Solvetheequations.Youmayuseyourcalculatortostart,syntheticdivision,factoring,orthe
quadraticformula.Leaveanswersasexactanswers
quadraticformula.Leaveanswersasexactanswersinsimplifiedform.
insimplifiedform.
orm.
14. 2$ 2 + 7$ 3 − 4$ − $ − 4 = 0
15. 4$ I − 16$ 2 + 7$ 3 = −12$ − 3$ − 18