How many complex roots does the equation below have?

Mathematics

1 answer:

Maslowich3 years ago

4 0

Answer:

The number of complex roots is 6.

Step-by-step explanation:

Descartes's rule of signs tells you that the number of positive real roots is 0. The number of negative real roots will be at most 2. The minimum value of the left side will be between x=0 and x=-1, but will never be negative. Thus all six roots are complex.

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The magnitude of x^3 will exceed the magnitude of x^6 only for values of x between -1 and 1. Since the magnitude of either of these terms will not be more than 1 in that range, the left-side expression must be positive everywhere.

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A florist can make a grand arrangement in 18 minutes or a simple arrangement in 10 minutes. The florist makes at least twice as

Colt1911 [192]

Answer:

See explanation

Step-by-step explanation:

Let x be the number of simple arrangements and y be the number of grand arrangements.

1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so

$x\ge 2y$

2. A florist can make a grand arrangement in 18 minutes $=\dfrac{3}{10}$ hour, then he can make y arrangements in $\dfrac{3}{10}y$ hours.

A florist can make a simple arrangement in 10 minutes $=\dfrac{1}{6}$ hour, so he can make x arrangements in $\dfrac{1}{6}x$ hours.

The florist can work only 40 hours per week, then

$\dfrac{3}{10}y+\dfrac{1}{6}x\le 40$

3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.

The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.

Total profit: $(10x+25y)

Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines $x=2y$ and $\dfrac{3}{10}y+\dfrac{1}{6}x=40$