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# 4.) Sketch a graph of a polynomial that would have: Help!

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4.) Sketch a graph of a polynomial that would have:

a.) 7 real zeros
b.) 5 real and 2 complex zeros
c.) 4 complex zeros
d.) 2 complex and 4 real zeros

Feb 10, 2019

#1
+2

a)  We can make up whatever we want

For the first....a possibility is    ( x - 3)^5 (x - 2)^2

[ We have repeated real zeroes, but the problem doesn't say that every zero has to be unique ]

The graph of this is here :   https://www.desmos.com/calculator/td0qq1sakf

b)  We can have

(x  - 3) ( x + 3) ( x - 4) ( x + 4) (x + 6) ( x^2 + 1)

The graph of this is here : https://www.desmos.com/calculator/0f8x7e1irp

c) We can have

(x^2 + 1) ( x^2 + 3)

Graph : https://www.desmos.com/calculator/sqj7sk0rcf

d) We can have

(x^2 + 1) (x + 3) ( x - 3) ( x + 2) ( x - 2)

Graph : https://www.desmos.com/calculator/nyabj6mmtz

I hope these links work, GM !!!   Feb 10, 2019
#2
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Thanks so much, CPhill! I wouldn't even know how to make polynomial with 7 real zeros.

Also, can you help me solve this problem? https://web2.0calc.com/questions/working-together-formula-3

I got my work written down but I want to make sure of if it is correct.

-- 7H3_5H4D0W

Feb 10, 2019
edited by GAMEMASTERX40  Feb 10, 2019
#3
+2

OK....using your formula from last week...we have

1/3 + 1/4  =  1/ Total Time Working Together

4/12  + 3/12 =  1 / T

7 /12  = 1 / T       [ remember that we can write ]

12 / 7  =  T / 1

12/ 7  = T

T = 12/7 hrs ≈     1.7 hrs  =    1 + .7(60)  =   1 hr 42 min   CPhill  Feb 10, 2019
#4
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Nice, my work makes sense now. Thanks!

-- 7H3_5H4D0W

GAMEMASTERX40  Feb 10, 2019
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+1   CPhill  Feb 10, 2019
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