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erik [133]
3 years ago
14

At most, how many unique roots will a third-degree polynomial function have?

Mathematics
1 answer:
beks73 [17]3 years ago
7 0

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)

But this is a fourth-degree polynomial.

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A scatterplot is used to display data for a runner where x is the number of miles run, and y is the time, in minutes, that it ta
larisa [96]

The interpretation of y = 9.5x is that: (a) For each 1 minute, the runner ran 9.5 miles.

<h3>How to interpret the equation?</h3>

The equation of the line of best fit is given as:

y = 9.5x

Divide both sides by x

9.5 = y/x

From the question, we have:

  • x ⇒ number of miles run
  • y ⇒ time

This means that:

9.5 = number of miles run/time

Hence, the interpretation of y = 9.5x is that: (a) For each 1 minute, the runner ran 9.5 miles.

Read more about scatter plots at:

brainly.com/question/6592115

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8 0
2 years ago
If Carl takes a pizza with 8 slices and has three friends eat a slice, what fraction of the pizza is left?
murzikaleks [220]
Ok so the wording is confusing

is it
A. 3 friends took 1 slice each (total is 3 slice) or
B. 3 friends took 1 slice total

if A, go to AAAAAA
if B. to to BBBBB


AAAAAAAAAA
3 slices taken
fraction is parts out of whole
what is left
left=original-taken
taken=3
original=8
8-3=5
5=left
fraction is 5/total=5/8


BBBBBB
taken=1
fraction is parts out of whole
what is left
left=original-taken
taken=1
original=8
8-1=7
7=left
fraction is 7/total=7/8





if 3 slices taken total then 5/8 left
if 1 slice taken totl then 7/8 left
8 0
3 years ago
Read 2 more answers
2x+14= -21-5x<br> Need to find out what x is but a step by step explanation please
adoni [48]
Notice how on both sides of the equation there is one coefficient (number being multiplied by x) and a constant (just a plain number). You want all constants to be on one side and all coefficients on the other. He’s how do to that:
2x+14=-21-5
I am choosing that all constants will be on the right side, so I will do the inverse operation of any constant on the left side to remove it. Here, a constant on the left side is 14. I will subtract 14 from both sides of the equation. Positive 14 minus 14 is zero, so it cancels out and removes it.
2x+14-14 = -21-5x
2x = -35-5x
See how the 14 is now gone? The equation looks much simpler now. Okay next, you can see that there is a coefficient on the “constant side” that I’ve chosen, so I am going to remove that. Negative 5 plus positive 5 equals zero. Do this on both sides of the equation.
2x+5x = -35-5x+5x
7x = -35
Now the equation is just two numbers. All that is left to do is divide by the last coefficient, 7, in this case.
7x/7 = -35/7
x = -5
8 0
1 year ago
Read 2 more answers
ASAP! I’ll give u Brainly !
kondor19780726 [428]

Answer:

I'm sorry but if your struggling with this iďk what to tell you chief

  • Its (1,5)
7 0
3 years ago
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Jerry started doing sit ups every day. The first day he did 18 sit ups. Every day after that he did 4 more sit ups than he had d
Alexandra [31]

Answer:

10

Step-by-step explanation:

6 0
2 years ago
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