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Paraphin [41]
3 years ago
6

Part 5: Identify key features and graph a hyperbola from general form.

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
3 0

First things first. I tried and really hope im correct.

A) (x+1)^2/9 – (y+2)^2/4 = 1

B) (-1,-2)

C) (-4.61, -2) and (2.61, -2)

D) y=2/3x-1.33333 and y=-2/3x-2.66666

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At most, how many unique roots will a third-degree polynomial function have?
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The fundamental theorem of algebra states that a polynomial with degree n has at most n solutions. The "at most" depends on the fact that the solutions might not all be real number.

In fact, if you use complex number, then a polynomial with degree n has exactly n roots.

So, in particular, a third-degree polynomial can have at most 3 roots.

In fact, in general, if the polynomial p(x) has solutions x_1,\ x_2,\ldots x_n, then you can factor it as

p(x) = (x-x_1)(x-x_2)\ldots (x-x_n)

So, a third-degree polynomial can't have 4 (or more) solutions, because otherwise you could write it as

p(x)=(x-x_1)(x-x_2)(x-x_3)(x-x_4)

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Select the correct answer. Which number has a terminating decimal expansion? A. 2/7 B.√12 C. 5/8 D. 2/11
quester [9]

Answer:

Option C is correct option.

Step-by-step explanation:

We need to determine which number has a terminating decimal expansion.

<em>Terminating decimal </em>

<em>A decimal number that contains a finite number of digits after the decimal point is called terminating decimal . </em>

<em>for example 0.123 is terminating decimal as it has finite number of digits after decimal point.</em>

Now, we will look at each option to find the terminating decimal

A. 2/7

Converting in decimal form: 0.28571....

As it doesn't contain finite numbers after decimal point, so 2/7 is not terminating decimal.

B.√12

Converting in decimal form: 3.46410....

As it doesn't contain finite numbers after decimal point, so √12 is not terminating decimal.

C. 5/8

Converting in decimal form: 0.625

As it contain finite numbers after decimal point, so 5/8 is terminating decimal.

D. 2/11

Converting in decimal form: 0.18181....

As it doesn't contain finite numbers after decimal point, so 2/11 is not terminating decimal.

Therefore, Option C is correct option.

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