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3 years ago

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Use the Rational Zeros Theorem to write a list of all potential rational zeros f(x) = 14x^3 + 56x^2 + 2x - 7

1 answer:

Crank3 years ago

3 0

The factors of 7are -1 and 7 or 1 and -7, the factors of 14 are 1, 2, 7, and 14, or -1, -2, -7,-14. so the list of potential zeros are: 1/1, 1/2, 1/7, 1/14, 7/1,7/2, 7/7, 7/14, which can be simplified into 1, 1/2,1/7, 1/14, 7, 7/2
add the negative ones: -1, -1/2,-1/7, -1/14, -7, -7/2
I believe there are a total of 12 potential zeros
reference:
http://www.sparknotes.com/math/algebra2/polynomials/section4.rhtml

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xxTIMURxx [149]

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Solution:

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Solve using mid-point formula:

$$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right )$

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<u>To find the missing coordinate:</u>

Let the missing coordinates by x and y.

Here $x_1=0, y_1=0, x_2=x, y_2=y$

$$\text{Midpoint}=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{x}{2}, \frac{y}{2}\right )$

Now equate the x-coordinate.

$$ \frac{m+h}{2}=\frac{x}{2}$

Multiply by 2 on both sides of the equation, we get

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x = m + h

Now equate the y-coordinate.

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Multiply by 2 on both sides of the equation, we get

n = y

y = n

Hence the missing coordinates of the parallelogram is (m + h, n).

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Read 2 more answers

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Keith_Richards [23]

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Step-by-step explanation:

The goal is to simplify this expression.

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I hope I helped!

Let me know if you need anything else!

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