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2 years ago

The graph of f(x)=2x^3+x^2-4x-2 is shown. How many of the roots of f(x) are rational

Mathematics

2 answers:

Alexeev081 [22]2 years ago

7 0

We can one theorem to help us find rational roots of this polynomial.

2x^3 + x^2 - 4x - 2

We'll use Descartes' rule of signs.

Because there is 1 sign change, 1 of the 3 roots will be positive.

Now we can make the value of x -1 to see how many negative roots there will be.

-2 + 1 + 4 - 2

There are 2 sign changes, so we know there will be 2 negative roots.

Because of this, we should have 3 real, rational roots.

ohaa [14]2 years ago

6 0

Answer:

The answer is 1

I don't know the step-by-step explanation

Step-by-step explanation:

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harina [27]

Answer:

The maximum variance is 250.

Step-by-step explanation:

Consider the provided function.

$V(x)=1000x(1-x)$

$V(x)=1000x-1000x^2$

Differentiate the above function as shown:

$V'(x)=1000-2000x$

The double derivative of the provided function is:

$V''(x)=-2000$

To find maximum variance set first derivative equal to 0.

$1000-2000x=0$

$x=\frac{1}{2}$

The double derivative of the function at $x=\frac{1}{2}$ is less than 0.

Therefore, $x=\frac{1}{2}$ is a point of maximum.

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Uma rede de supermercados fornece a seus clientes um cartão de crédito cuja identificação é formada por 3 letras distintas (dent

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Answer:

The correct option is (A) 33,600.

Step-by-step explanation:

The question is:

A supermarket chain provides its customers with a credit card whose identification is formed by 3 different letters (among 26), followed by 4 different digits. A given city will receive cards with L as the third letter, the last number is zero and the penultimate is 1. The total number of distinct cards offered by such supermarket chain for that city is A) 33600 B) 37800 C) 43200 D ) 58500 E) 67600

Solution:

The general format of the credit cards provided by a supermarket chain is as follows:

X X X # # # #

Here, X represents letters and # represents numbers.

All the three letters have to different and all the four numbers have to different, i.e. no repetition allowed.

It is provided that a given city will receive cards with L as the third letter, the last number is zero and the penultimate is 1.

Then the general format of this cities credit cards is as follows:

X X L # # 1 0

Now there are two spaces left for letters and 2 for numbers.

As there are no repetition allowed the two letter spaces can be filled by:

Number of ways to select 2 letters = 25 × 24 = 600

And the number of ways to select two numbers when there is no repetition allowed is:

Number of ways to select 2 numbers = 8 × 7 = 56

Compute the total number credit cards available at the supermarket as follows:

Total number credit cards = 600 × 56 = 33600

Thus, the total number of distinct cards offered by such supermarket chain for that city is 33,600.

The correct option is (A).

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