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max2010maxim [7]
2 years ago
15

Find a degree 3 polynomial whose coefficient of x^3 equal to 1. The zeros of this polynomial are -5, -4i, and 4i. Simplify your

answer so that it has only real numbers as coefficients.
I got an answer by solving (x^3+5x^2-16x-80) but it says thats incorrect.​
Mathematics
1 answer:
borishaifa [10]2 years ago
7 0

Answer:

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

Step-by-step explanation:

You know that you can write your polynom this way : (x-r1)(x-r2)(x-r3) with r1,r2 and r3 the roots so you get :

(x+5)(x+4i)(x-4i)

Simplify (x+4i)(x-4i) with the formula (a-b)(a+b)=a²-b²

so you have (x^2+16)=(x+4i)(x-4i)

Your polynom looks like this :

(x^2+16)(x+5) just expand it

and you get x^3+5x^2+16x+80

You might be interested in
Which of the following is true?
EleoNora [17]
The options can be rewrited as follow:
A. 5<4
B. 5<5
C. 5<4
D. 4<-5

∴ Answer is none of the above.

Unless perhaps you have written down the question incorrectly.
8 0
3 years ago
The cake density is 0.454 ounce per cubic inch and the fair price is $0.20 per ounce. What should be a fair price for each cake?
aleksklad [387]

Answer:

price = x * 0.2

or

price = x * 0.454 * 0.2

Step-by-step explanation:

In this case we must know either the mass of the cake or its volume.

Given the case that we know the mass of the cake, it would be:

price = x * 0.2

where x is the mass of the cake in ounces, that is to say if for example a cake has a mass of 10 ounces, it would be:

price = 10 * 0.2 = 2

which means that each cake costs $ 2

Given the case of the volume, we must first multiply the density by this volume in order to calculate the mass and finally the price.

price = x * 0.454 * 0.2

where x is the volume of the cake in cubic inches, if for example the volume is 10 cubic inches it would be:

price = 10 * 0.454 * 0.2 = 0.908

which means that each cake costs $ 0.9

5 0
3 years ago
Factor completely 3x^2 − x − 4.
ozzi

3x^2 − x − 4

factor

= (3x − 4)(x + 1)


answer

D. (3x − 4)(x + 1)

8 0
3 years ago
1. A system of linear equations that has one solution has slopes that are__________
algol13

Answer:

different

Step-by-step explanation:

different slopes gives one solution

same slopes with different constant has no solution

same slopes and constants has many solutions

3 0
3 years ago
Robert's dog is 4 years older than Karen's cat. In 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. How
mylen [45]

Answer:

5.5 years old.

Step-by-step explanation:

Let D represent present age of Robert's dog and C represent present age of Karen's cat.

We have been given that Robert's dog is 4 years older than Karen's cat. We can represent this information in an equation as:

D=C+4...(1)

We are also told that in 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. After 3 years age of dog and cat would be D+3 and C+3 respectively.

We can represent this information in an equation as:

D+3+C+3=13...(2)

From equation (1), we will get:

C=D-4

Upon substituting this value in equation (2), we will get:

D+3+D-4+3=13

Combine like terms:

2D+2=13

2D+2-2=13-2

2D=11

\frac{2D}{2}=\frac{11}{2}

D=5.5

Therefore, Robert's dog is 5.5 years old right now.

3 0
3 years ago
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