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Zanzabum
3 years ago
13

Solve the following equation by identifying all of its roots including all real and complex numbers. In your final answer, inclu

de the necessary steps and calculations. Hint: Use your knowledge of factoring polynomials.
(x^2+1)(x^3+2x)(x^2-64)=0
Mathematics
1 answer:
atroni [7]3 years ago
3 0
X² + 1 = 0
x² = - 1
x 1 = i,  x 2 = - i
x³ + 2 x = 0
x ( x² + 2 ) = 0
x 3 = 0
x² + 2 = 0
x² = - 2
x 4 = √2 i,  x 5 = - √2 i
x² - 64 = 0
x² = 64
x 6 = - 8,   x 7 = 8
Answer:
All roots are: { -√2 i,   -i,   i,   √2 i,   - 8,   0,   8 }
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Answer:

S'(t) = 0.09t^2 + t + 9

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S'(11) = 30.89 means that, 11 months from now, the rate at which sales change is $30,890,000 per month

Step-by-step explanation:

The derivate of the sales function S'(t) , which is the rate at which sales vary with time in months, is:

\frac{dS(t)}{dt} =S'(t) = 0.09t^2 + t + 9

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S'(2) is found by applying t=2 to S'(t):

S'(2) = 0.09*(2^2) + 2 + 9\\S'(2) = 11.36

Since the sales function gives the amount of sales in millions of dollars,

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S'(t) represents the rate of change in sales in millions of dollars per month.

S'(11) = 30.89 means that, 11 months from now, the rate at which sales change is $30,890,000 per month

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