All categories

4 years ago

Which of the following is a polynomial with roots 5, 4i, and -4i?

Mathematics

1 answer:

solniwko [45]4 years ago

8 0

The correct answer is x^3 - 5x^2 + 16x - 80.

In order to find this, we work backwards. Start by creating true statements for each of the roots.

x = 5

x = +/-4i

Now we can solve all of these until they are statements that equal 0.

x = 5 ----> Subtract 5 from both sides

x - 5 = 0

x = +/-4i ------> Square both sides

x^2 = -16 ---> Add 16 to both sides.

x^2 + 16 = 0

Now we can use the two statements that we have and multiply them to get the polynomial.

(x - 5)(x^2 + 16)

x^3 - 5x^2 + 16x - 80

You might be interested in

What is the probability of not rolling a 5 on a standard number cube?

Angelina_Jolie [31]

A standard number cube has 6 sides....

probability of rolling a 5 is 1/6......probability of not rolling a 5 is 5/6

8 0

3 years ago

Read 2 more answers

Please help me ASAP y’all!!!

solong [7]

The answer is C) 126

3 0

3 years ago

I don’t know how I would simply this

zlopas [31]

It is 11m+8

You just combine like terms

7 0

3 years ago

In 1990, the mean duration of long-distance telephone calls originating in one town was 7.2 minutes. A long-distance telephone c

scoundrel [369]

Answer:

We know that In 1990, the mean duration of long-distance telephone calls originating in one town was 7.2 minutes. And we want to test if the mean duration of long-distance phone calls has changed from the 1990 mean of 7.2 minutes (alternative hypothesis) and the complement rule would represent the null hypothesis.

The correct system of hypothesis are:

Null hypothesis: $\mu =7.2$

Alternative hypothesis: $\mu \neq 7.2$

So then the best option for this case would be:

H0: μ = 7.2 minutes Ha: μ ≠ 7.2 minutes

Step-by-step explanation:

The correct system of hypothesis are:

Null hypothesis: $\mu =7.2$

Alternative hypothesis: $\mu \neq 7.2$

So then the best option for this case would be:

H0: μ = 7.2 minutes Ha: μ ≠ 7.2 minutes

And in order to test the hypothesis we can use a one sample t test or z test depending if we know the population deviation or not

4 0

3 years ago

Find all subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2•

sasho [114]

All subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2 is

{( 0,1) (-1,1)}

{(1,0)(0,1)}

{(1,0)(-1,1)}

A fixed A is a subset of some other set B if all elements of set A are factors of set B. In other phrases, set A is contained within set B. The subset relationship is denoted as A⊂B.

Subsets are a part of one of the mathematical ideas known assets. a hard and fast is a set of items or factors, grouped within the curly braces, consisting of {a,b,c,d}. If a set A is a set of even numbers and set B includes {2, 4,6}, then B is stated to be a subset of A, denoted by B⊆A and A is the superset of B.

In mathematics, set A is a subset of a fixed B if all factors of A are also elements of B; B is then a superset of A. It's far possible for A and B to be equal; if they may be unequal, then A is a proper subset of B. The relationship of one set being a subset of every other is known as inclusion.

A set which is (is linearly independent andoil generates/ spans the space (like R) is called a baris.

S= (1,0), (0,1), (-1))}

option-1

As, dimension of R²=2, so, Ary set

conists of three vectors cannot be baris for R²

so, option-1 is wrong.

option-2

As, dimention of R2-2.

{(10), (-11)} is a linearly independent

subset of S. so And as, this subset

has 2 vectors so it will as also

span R se, it will be a baris

of IR?

So, option-6 is correct

{(0,1)} is linearly independent subset

option-7

As (LO) has one vector. So, it cannot

Span/generate R so, it also cannot be balis

for R2

of S.

But it cannot span R²

So ut cannot

be a baris of R2

se, option-2 is wrong.

Option-3

AS, {(0,1), (-1,1)} is linearly independent

So, option -7, is wrong.

Answer

[as fox amy KER, (-1,1) K (0,1)] subset of s

And also as dim {(0,1), (-11)}=2

which is same as the dimention of IR2

so {(0,1), (-11)} forms a baris of R2

{(1,0), (0,1), (-11)}

{(1,0)}

So, option-3 is

Connect

option-4

{(1,0), (3, 1)} is standard balis of R2

which is subset of S.

[{(1,0), (0,1)}]

So, option-4 is correct.

option-5

{(-11)}

consists of one vertex,

so, ut cannot span R², so, ut cannot

be a baris of R²

9090

LO {(1,0), (-1,1)}]

Learn more about subsets here brainly.com/question/2000547

#SPJ4

7 0

2 years ago