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Sever21 [200]
3 years ago
8

A) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list.

Mathematics
1 answer:
lara31 [8.8K]3 years ago
6 0

Answer:

steps below

Step-by-step explanation:

x⁶ - 7x³ - 8 = (x⁶ + x³) - (8x³ + 8)

                  = x³ (x³+1)-8(x³+1)

                  = (x³ - 2³)(x³ + 1)

                  = (x-2)(x²+2x+4)(x+1)(x²-x+1)

(x-2)(x²+2x+4)(x+1)(x²-x+1) = 0

<u>x= -1 or x = 2</u>   ... roots

or    x²+2x+4=0   or    x²-x+1=0  

x²+2x+4=0

x = (-2±√4-16)/2 = <u>-1 ± √3 i</u>   ... complex roots

x²-x+1=0

x = (1±√1-4)/2 = <u>1/2 ± (√3)i / 2</u>   ... complex roots

<u />

b) P(x) = x⁶ - 7x³ - 8

           = <u>(x-2)(x²+2x+4)(x+1)(x²-x+1)</u>

           = (x+1)(x-2)(x-(-1 + √3 i))(x-(-1 - √3 i)(x-(1/2 + (√3)i / 2))(x-(1/2 - (√3)i / 2))

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The linear function that represent the cost per pound of the gummy bears in x years after 2000 is given by:

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<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

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In this problem, we have that:

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Thus, the function is:

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