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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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What is the probability that a client chooses Greece, or Italy, or both countries, on a tour?
Jlenok [28]

Answer:

Both

Step-by-step explanation:

5 0
3 years ago
Mr. Clark traveled 456.4 km in 14 days.
xeze [42]

\qquad \qquad\huge \underline{\boxed{\sf Answer}}

<h3><u>Distance travelled each day is</u> : </h3>

  • 32.6 km

<h3><u>Explanation</u> : </h3>

Distance travelled in 14 days is : 456.4 km

And if he travels same Distance each day, so let the Distance travelled on each day be x

According to question ~

\qquad \sf  \dashrightarrow \: 14 \times x = 456.4

\qquad \sf  \dashrightarrow \: x = 456.4 \div 14

\qquad \sf  \dashrightarrow x = \: 32.6  \: \: km

So, he travels 32.6 km per day

5 0
2 years ago
9 3 -3/4 -10 1/2 -1.75 least to greatest
Mazyrski [523]

-10, -1.75, -3/4, 1/2, 3, 9

_____________________________

-3/4 converts to -0.75,

and 1/2 converts to 0.5. With -10 being farthest from zero on the number line, it would be the smallest. -1.75 would be the second smallest. Keeping in mind that -3/4 converts to -0.75, it would be the 3rd smallest. 1/2, or 0.5 would be greater, as it is the smallest POSITIVE number. Then you do 3, as it as a whole number, but still not the greatest. 9 would be the greatest.

hope i was helpful;-)

5 0
3 years ago
7 times a number is 8 less than the square of that number. Find the negative solution.
charle [14.2K]

Answer:

  -1

Step-by-step explanation:

The required relation is ...

  7n = n^2 -8

  0 = n^2 -7n -8 . . . . put in standard form

  0 = (n -8)(n +1) . . . . factor

Solutions are n=8 and n=-1.

The negative solution is -1.

7 0
3 years ago
Find the product of 2x^4(4x^2 + 3x + 1).
lianna [129]
We want to find the product:

                         \displaystyle{ 2x^4\cdot(4x^2 + 3x + 1).

By the \text{Distributive property}, we distribute 2x^4 over each of the three terms inside the parenthesis:

\displaystyle{ 2x^4\cdot(4x^2 + 3x + 1)=2x^4\cdot4x^2+2x^4\cdot3x+2x^4\cdot1.

Multiplying the coefficients, and adding the exponents we get:

8x^6+6x^5+2x^4.


Answer: 8x^6+6x^5+2x^4.
5 0
3 years ago
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