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maria [59]
2 years ago
13

Find a third degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one.

Mathematics
1 answer:
Tanzania [10]2 years ago
6 0

Answer:

The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is p(x) = x^{3}-5\cdot x^{2}-6\cdot x.

Step-by-step explanation:

From Fundamental Theorem of Algebra, we remember that the degree of the polynomials determine the number of roots within. Since we know three roots, then the factorized form of the polynomial function with the lowest degree is:

p(x) = (x-r_{1})\cdot (x-r_{2})\cdot (x-r_{3}) = 0 (1)

Where r_{1}, r_{2} and r_{3} are the roots of the polynomial.

If we know that r_{1} = -1, r_{2} = 0 and r_{3} = 6, then the polynomial function in factorized form is:

p(x) = (x+1)\cdot x \cdot (x-6) (2)

And by Algebra we get the standard form of the function:

p(x) = x\cdot (x+1)\cdot (x-6)

p(x) = x\cdot (x^{2}-5\cdot x -6)

p(x) = x^{3}-5\cdot x^{2}-6\cdot x (3)

The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is p(x) = x^{3}-5\cdot x^{2}-6\cdot x.

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Let’s see, for 6 servings he needed 4 carrots, meaning every carrot was equal to 1.5 servings. 15/1.5 is 10, 10 carrots for 15 servings.
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2 years ago
The sum of three consecutive positive numbers is 147. Find the product of the greatest and the
Dima020 [189]

Answer:

2400

Step-by-step explanation:

x+y+z=147

x+(x+1)+(x+2)=147

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x=48

The three consecutive positive numbers are 48, 49, and 50.

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2 years ago
Thirty-two percent of fish in a large lake are bass. Imagine scooping out a simple random sample of 15 fish from the lake and ob
klio [65]

Answer:

Thirty-two percent of fish in a large lake are bass. Imagine scooping out a simple random sample of 15 fish from the lake and observing the sample proportion of bass. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.

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B. The standard deviation is 0.8795. The 10% condition is not met because there are less than 150 bass in the lake.

C. The standard deviation is 0.1204. The 10% condition is met because it is very likely there are more than 150 bass in the lake.

D. The standard deviation is 0.1204. The 10% condition is not met because there are less than 150 bass in the lake.

E. We are unable to determine the standard deviation because we do not know the sample mean. The 10% condition is met because it is very likely there are more than 150 bass in the lake

The answer is E.

6 0
3 years ago
Can you guys figure out the linear function for this table, please?
Bess [88]

Answer:

y = 6x + 10

Step-by-step explanation:

This is because the slope is 6 and the y intercept is 10, therefore the answer is y = 6x + 10

5 0
2 years ago
My friend needs help explaining this and I don't know anything.
DIA [1.3K]

To solve this equation (correct me if i'm wrong), you could first multiply the bottom equation by 3, to get 15y. After that, we get -4x-15y=-17 and -3x + 15y=-39, and if we add the 2 equations up, on top of each other, we get -7x=-56, and we can conclude that x=8, and with substitution (-32 - 15y = -17), we know that y=(-1)


Here's what I mean by on-top


-4x-15y=-17

-3x + 15y=-39


-7x=-56

7 0
3 years ago
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