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o-na [289]
3 years ago
9

according to the fundemental theorem of algebra, how many roots exist for the polynomial function? f(x) = (x^3-3x+1)^2

Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
3 0

Answer:

6

Step-by-step explanation:

First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.

Expanding, we get

(x³-3x+1)²  = (x³-3x+1)(x³-3x+1)

= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1

= x^6 - 6x^4 + 2x³ +9x²-6x + 1

In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots

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What is the measure of what is the measure of (either 50,90,95, or 115)
Anuta_ua [19.1K]

Answer:

65 & 115

Step-by-step explanation:

<EGF = (180 - 50) /2 = 65 degree

<CGF = 180 - 65 = 115 degree

5 0
3 years ago
Show steps solving this problem 173×797=
Contact [7]
If the problem is
 (17 ^ 3) * (79 ^ 7) 
 The steps are: 
 Step 1:
 (17 ^ 3) = 4913
 Step 2:
 (79 ^ 7) = 1.92039E + 13
 Step 3:
 (4913) * (1.92039E + 13) = 9.43488E + 16

 If the problem is 
 (173) * (797)
 Step 1: 
 Multiply both terms with a calculator:
 (173) * (797) = 137881
8 0
3 years ago
The histogram below shows the heights, rounded to the nearest inch, of the members of the Oak High School basketball team. A. 1
Elan Coil [88]

Answer:

Range of player's height = 9 inch

Step-by-step explanation:

Given:

Number of players    Height range

4                                     66-67

8                                     68 -69

14                                    70-71

9                                     72-73

1                                      74-75

Find:

Range of player's height

Computation:

Range = Maximum value - Minimum Value

Range of player's height = Maximum height of a player - height of a player

Range of player's height = 75 inch - 66 inch

Range of player's height = 9 inch

5 0
2 years ago
Plz help I will give you BRAINLIESt 5stars
Svetradugi [14.3K]

Answer:

I will just give you the way of solving it

Step-by-step explanation:

First you have to change the sgape of the equation and it will become like this :

-6y=-2x+12

And then:

Y=0.33x+2

And then you have to give values to x and find y

For example i will make x zero (0)

It will become

Y=0.33(0)+12

=+12

And the points are (0,+12)

Go on like this and draw the line

Good luck

Sorry for bad english

4 0
3 years ago
What is the completely factored form of x4 8x2 – 9?
Alinara [238K]

For this case we have the following polynomial:

x ^ 4 + 8x ^ 2 - 9

We make the following change of variables:

u = x ^ 2

Rewriting we have

u ^ 2 + 8u - 9

Factoring the second order polynomial we have:

(u + 9) (u-1)

Then, returning the change we have:

(x ^ 2 + 9) (x ^ 2-1)

Finally, we factor the expression in the parentheses of the second term:

(x ^ 2 + 9) (x + 1) (x-1)

Answer:

the completely factored form is:

(x ^ 2 + 9) (x + 1) (x-1)

7 0
3 years ago
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