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vitfil [10]
3 years ago
10

Use the drawing tool(s) to form the correct answer on the provided number line.

Mathematics
1 answer:
miskamm [114]3 years ago
7 0

Answer:

x= 1, x= 4, and x= -3

Step-by-step explanation:

Use the possible combinations of factors of the constant term of the polynomial to find a first root. Try 1, -1, 2, -2, 3, -3, etc.

Notice in particular that x = 1 is a root (makes f(1) = 0):

f(1)=x^3-2*1^2-11*1+12=1-2-11+12=13-13=0

So we know that x=1 is a root, and therefore, the binomial (x-1) must divide the original polynomial exactly.

As we perform the division, we find that the remainder of it is zero (perfect division) and the quotient is: x^2-x-12

This is now a quadratic expression for which we can find its factor form:

x^2-x-12=x^2-4x+3x-12=x(x-4)+3(x-4)=(x-4)*(x+3)

From the factors we just found, we conclude that x intercepts (zeroes) of the original polynomial are those x-values for which each of the factors: (x-1), (x-4) and (x+3) give zero. That is, the values x= 1, x= 4, and x= -3. (these are the roots of the polynomial.

Mark these values on the number line as requested.

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Help me out here guys
kvasek [131]
D.

f(x) can be written as (x+2)(x-2)(x-1)
by using difference of two squares to expand x^2 - 4 whch yields 3 x intercepts

similarly, k(x) can be written as
x(x+5)(x-5) which also yields 3
x intercepts (0,-5, and 5)
3 0
2 years ago
The lowest recorded temperature in a town was 4ºF, without the windchill. With the wind, the temperature felt like 10ºF below ze
deff fn [24]

Answer:

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Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What is the distance from the point (a, −b, −4) to the origin?
laiz [17]

Answer:

  \sqrt{a^2+b^2+16}

Step-by-step explanation:

The distance (d) between two points in 3 dimensions is ...

  d = √((x2 -x1)² +(y2 -y1)² +(z2 -z1)²)

Then the distance between (a, -b, -4) and (0, 0, 0) is ...

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6 0
3 years ago
Please Answer Correctly To Get Brainliest. Wrong Answers WILL BE REPORTED.
frozen [14]
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7 0
3 years ago
How many ways are there to select 12 countries in the United Nations to serve on a council if 3 are selected from a block of 45,
sattari [20]

Answer: There are 2346953264 ways to do so.

Step-by-step explanation:

Since we have given that

Total number of selected countries = 12

Number of selected countries from a block of 45 = 3

Number of selected countries from a block of 57 = 4

So, remaining number of selected countries from a block of 69.

So, 12-(3+4)=12-7=5

Now, we need to find the number of ways, so we will use "Combination" to select that number of countries.

So, it becomes.

^{45}C_3\times ^{57}C_4\times ^{57}C_5\\\\=14190\times 395010\times 4187106\\\\=2346953264

Hence, there are 2346953264 ways to do so.

8 0
3 years ago
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