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sweet [91]
2 years ago
5

Find the zeros for: f(x)=x^4+x^3+4x^2 (Please show work)

Mathematics
2 answers:
mixas84 [53]2 years ago
6 0

View the image to see how I solved this problem.

Tanya [424]2 years ago
6 0

There is an obvious factor of x², so we can reduce this to the problem of finding zeros of a quadratic by factoring that out. Then, we can determine the zeros of the quadratic factor to complete the finding of zeros for the function.

A factor of x² can be factored out, leaving ...

... f(x) = x²(x² +x +4)

The latter factor has only complex zeros. It can be rewritten by completing the square.

... x² +x +4 = (x² +x +1/4) +(3 3/4) = (x +1/2)² +(3 3/4)

So, the real zeros are where x² = 0, at x = 0. The complex zeros are where the above expression is zero, ...

... (x +0.5)² +3.75 = 0

... (x +0.5)² = -3.75

... x + 0.5 = √-3.75 = ±0.5i√15

... x = -0.5(1 ±i√15)

The function zeros are 0 (multiplicity 2) and -0.5±0.5i√15.

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Find two positive integers such that the sum of the first number and four times the second number is 1000, and the product of th
vladimir2022 [97]

Answer:

The two numbers are:

x = 500

y = 125

Step-by-step explanation:

We want to find two numbers x and y, such that:

x + 4*y = 1000

f(x, y) = x*y is maximum.

From the first equation, we can isolate one of the variables to get

x = 1000 - 4y

now we can replace it in f(x, y):

x*y = (1000 - 4*y)*y  = 1000*y - 4*y^2

So now we want to maximize the function:

f(y) =- 4*y^2 + 1000*y

where y must be an integer.

Notice that this is a quadratic equation with a negative leading coefficient (so the arms of the graph will open downwards), thus, the maximum will be at the vertex.

Remember that for a general quadratic equation:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/(2*a)

so, in the case of:

f(y) =- 4*y^2 + 1000*y

the y-value of the vertex will be:

y = -1000/(2*-4) = 1000/8 = 125

So we found the value of y.

now we can use the equation:

x = 1000 - 4*y

x = 1000 - 4*125 = 1000 - 500 = 500

x = 500

Then the two numbers are:

x =500

y = 125

6 0
2 years ago
Write a biconditional statement to define the term parallelogram
son4ous [18]
In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.



Hope this helps :)
6 0
2 years ago
Which of the k values are solutions to the following equation?<br> k2 = 0.49
madam [21]
C and D bc +-0.7 is the answer
but because there no answer which contains both i think u should mark E
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The correct answer is 0.78. Hope this helps.
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maw [93]
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