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3 years ago

If one of the zeros of the cubic polynomial x3 + ax2 + bx + c is -1, then what will be the product of the other two zeros?

Mathematics

1 answer:

zhenek [66]3 years ago

6 0

Answer:

The product of the other two zeros is c

Step-by-step explanation:

Let α, β and γ be the zeros of the polynomial x³ + ax² + bx + c. Since one of the zeros is -1, therefore let γ = -1. Hence:

sum of the roots = α + β + γ = -a

-1 + β + γ = -a

β + γ = -a + 1

αβ + αγ + βγ = b

-1(β) + (-1)γ + βγ = b

-β -γ + βγ = b

Also, the product of the zeros is equal to -c, hence:

αβγ = -c

-1(βγ) = -c

βγ = c

Hence the product of the other two zeros is c

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Fill in the missing number to complete the linear equation that gives the rule for this table. Explain/show how you got your ans

Aneli [31]

Answer:

y = x - 1

Step-by-step explanation:

To create a linear equation in the slope-intercept form, which is in the form of y = mx + b, we need to find the slope/rate of change, m, and the y-intercept, b.

Rate of change can be calculated using two pairs, (3, 2) and (4, 3)

Rate of change/slope (m) = $\frac{f(b) - f(a)}{b - a}$ ,

Where,

b = 4

f(b) = 3

a = 3

f(a) = 2

Plug in the values

$\frac{3 - 2}{4 - 3} = \frac{1}{1}$

m = 1

Plug in x = 3, y = 2 and m = 1 into y = mx + b

2 = 1(3) + b

Solve for b

2 = 3 + b

Subtract 3 from each side

2 - 3 = b

-1 = b

b = -1

Substitute m = 1 and b = -1 into y = mx + b.

y = 1(x) +(-1)

y = x - 1

The linear equation that gives the rule for this table is y = x - 1

8 0

3 years ago

HELP!!<br> Which table is a probability distribution table?

fomenos

Answer:

Table 1 is the only table which represents PROBABILITY DISTRIBUTION table.

Step-by-step explanation:

In any given probability distribution:

1) The probability of each event should be strictly POSITIVE.

2) Sum of all events in a a distribution should be 1.

Now, here

A) All of the values of probability (0.11, 0..5, 0.49,0.35) are positive.

Also, 0.11 + 0.5 + 0.49 + 0.35 = 1

So, the given table is a PROBABILITY DISTRIBUTION.

B)The table is NOT a PROBABILITY DISTRIBUTION as here

P(Blue) = -1, which is negative.

C)The table is NOT a PROBABILITY DISTRIBUTION as here

P(Green) = -0.49, which is negative.

D)The table is NOT a PROBABILITY DISTRIBUTION as here

P(Purple) = -0.1, which is negative.

Hence, table 1 is the only table which represents PROBABILITY DISTRIBUTION table.

3 0

3 years ago

according the the american hotel and motel association, women are expected to account for half of all business travelers by the

Slav-nsk [51]

Answer: 0.71221

Step-by-step explanation:

We know that for binomial distribution :-

$\mu=np\ \ ;\ \sigma=\sqrt{np(1-p)}$ , where p is the proportion of success in each trial and n is the sample size.

Given : p=0.80 ; n=20

Then, $\mu=20(0.8)=16\ \ ;\ \sigma=\sqrt{20(0.8)(0.2)}=1.79$

Let X be the binomial variable.

z-score : $z=\dfrac{x-\mu}{\sigma}$

For x=9

$z=\dfrac{9-16}{1.79}=-3.91$

For x=17

$z=\dfrac{17-16}{1.79}=0.56$

Then, the probability that more than 9 but less than 17 of the hotels in the sample is given by :-

$P(9$

Hence, the probability that more than 9 but less than 17 of the hotels in the sample = 0.71221

5 0

3 years ago

Gilbert is graduating from college in twelve months, but he will need a loan in the amount of $5,125 for his last two semesters.

FrozenT [24]

<span>Stafford: $ 5,673.71 PLUS: $ 5,539.36</span>

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3 years ago

A university has ten dormitories for students. All of the dormitories have students of similar ages and offer the same convenien

lina2011 [118]

Answer:

a is correct

Step-by-step explanation:

4 0

2 years ago