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12345 [234]
3 years ago
12

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=   --------------------------------

                        8

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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(5/3) (0.60)^3(0.40)^2

Step-by-step explanation:

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How do I turn 1/4 into a decimal?​
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Answer:

No problem ;)

Step-by-step explanation:

1/4: 0.25

2/4:0.50

3/4: 0.75

4/4(1): 1

<em>Hope </em><em>this</em><em> </em><em>helps </em><em>you!</em>

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Calculate a length of a square ground of perimeter 160m​
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5 0
3 years ago
A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tic
dalvyx [7]

Answer:

The expected revenue of the tour operator is 985.

Step-by-step explanation:

There are two outcomes:

Either less than 21 tourists show up and the operator does not have to pay anything. Or 21 tourists show up and the operator has to repay 100.

Anyways, initially he gets the price of all the tickets sold. That is 21 each at 50, so R = 21*50 = 1050.

Then, we need to find the probability that all of the 21 tourists show up. In this case, we have to subtract 100 from the revenue.

Each tourist has a 0.02 probability of not showing up. This means that each has a 1-0.02 = 0.98 probability of showing up. So the probability P that all 21 tourists show up is P = (0.98)^{21} = 0.6542.

So, the expected revenue of the tour operator is

R = 1050 - 100P = 1050 - 100(0.6542) = 984.58

Rounded up, the expected revenue of the tour operator is 985.

6 0
3 years ago
Given the diagram below, what is m/B?
Radda [10]

Answer:

115°

Step-by-step explanation:

The above shape is a quadrilateral.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

The sum of interior angles of a Quadrilateral is 360°

Therefore,

115 + 65 + 65 + m = 360

245 + m = 360

m = 360 - 245

m = 115°

Therefore, m< B = 115°

7 0
2 years ago
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