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3 years ago

Factor 4x^4+7x^2-2=0

Mathematics

1 answer:

natulia [17]3 years ago

6 0

Answer:

(2x-1)(2x+1)(x^2+2) = 0

Step-by-step explanation:

Here's a trick: Use a temporary substitution for x^2. Let p = x^2. Then 4x^4+7x^2-2=0 becomes 4p^2 + 7p - 2 = 0.

Find p using the quadratic formula: a = 4, b = 7 and c = -2. Then the discriminant is b^2-4ac, or (7)^2-4(4)(-2), or 49+32, or 81.

Then the roots are:

-7 plus or minus √81

p= --------------------------------

p = 2/8 = 1/4 and p = -16/8 = -2.

Recalling that p = x^2, we let p = x^2 = 1/4, finding that x = plus or minus 1/2. We cannot do quite the same thing with the factor p= -2 because the roots would be complex.

If x = 1/2 is a root, then 2x - 1 is a factor. If x = -1/2 is a root, then 2x+1 is a factor.

Let's multiply these two factors, (2x-1) and (2x+1), together, obtaining 4x^2 - 1. Let's divide this 4x^2 - 1 into 4x^4+7x^2-2=0. We get x^2+2 as quotient.

Then, 4x^4+7x^2-2=0 in factored form, is (2x-1)(2x+1)(x^2+2) = 0.

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What is the value of x in the equation 2.5 minus 0.25 x = negative 3

Dafna11 [192]

Answer:

-22

Step-by-step explanation:

4 0

3 years ago

At an airport, it cost 7 to park for one hour and 5 per hour for each additional hour.Let x represent the number hours parked.wr

kompoz [17]

The cost of parking is an initial cost plus an hourly cost.
The first hour costs $7.
You need a function for the cost of more than 1 hour,
meaning 2, 3, 4, etc. hours.
Each hour after the first hour costs $5.

1 hour: $7
2 hours: $7 + $5                  = 7 + 5 * 1          = 12
3 hours: $7 + $5 + $5          = 7 + 5 * 2          = 17
4 hours: $7 + $5 + $5 + $5 = 7 + 5 * 3          = 22

Notice the pattern above in the middle column.
The number of $5 charges you add is one less than the number of hours.
For 2 hours, you only add one $5 charge.
For 3 hours, you add two $5 charges.

Since the number of hours is x, according to the problem, 1 hour less than the number of hours is x - 1.

The fixed charge is the $7 for the first hour.
Each additional hour is $5, so you multiply 1 less than the number of hours,
x - 1, by 5 and add to 7.

C(x) = 7 + 5(x - 1)

This can be left as it is, or it can be simplified as

C(x) = 7 + 5x - 5

C(x) = 5x + 2

Answer: C(x) = 5x + 2

Check:
For 2 hours: C(2) = 5(2) + 2 = 10 + 2 = 12
For 3 hours: C(3) = 5(3) + 2 = 15 + 2 = 17
For 4 hours: C(3) = 5(4) + 2 = 20 + 2 = 22
Notice that the totals for 2, 3, 4 hours here
are the same as the right column in the table above.

6 0

3 years ago

What is the frequency of the graph of y = 1/3 sin(2x)?

vovangra [49]

Given:

The sine function is:

$y=\dfrac{1}{3}\sin (2x)$

To find:

The frequency of the graph of given function.

Solution:

If a sine function is defined as:

$y=A\sin(Bx+C)+D$

Then, the frequency of the sine function is:

$f=\dfrac{B}{2\pi}$

We have,

$y=\dfrac{1}{3}\sin (2x)$

Here, $B=2$ . So, the frequency of the given function is:

$f=\dfrac{2}{2\pi}$

$f=\dfrac{1}{\pi}$

Therefore, the correct option is D.

3 0

2 years ago

P: It's sunny.

lapo4ka [179]

Answer:

I think the answer is c

Step-by-step explanation:

please give me brainlist

5 0

3 years ago

What are the domain restrictions of the function f(x) = the quantity of x squared plus 6x plus 9, all over 3x plus 15.

dangina [55]

Answer:

x = - 5

Step-by-step explanation:

Given

f(x) = $\frac{x^2+6x+9}{3x+15}$

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve : 3x + 15 = 0 ⇒ 3x = - 15 ⇒ x = - 5 ← excluded value

Domain x ∈ R , x ≠ - 5

6 0

3 years ago