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AysviL [449]
4 years ago
14

What are the real and complex solutions of the polynomial equation X^3-216=0

Mathematics
1 answer:
vazorg [7]4 years ago
3 0

Answer:

6,\ -3+3\sqrt{3}i,\ -3-3\sqrt{3}i

Step-by-step explanation:

Factor the equation x^3-216=0 using formula for difference of the cubes:

x^3-216=(x-6)(x^2+6x+36),

then

x-6=0\ or\ x^2+6x+36=0.

1. The equation x-6=0 has real solution x=6.

2. The equation x^2+6x+36=0 has negative discriminant D=6^2-4\cdot 36=36-144=-108, then it has two complex solutions

x_{1,2}=\dfrac{-6\pm 6\sqrt{3}i}{2}=-3\pm3\sqrt{3}i.

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Solve for x. Write both solutions, separated by a<br>comma.<br>6x2 + 5x - 14 = 0​
Igoryamba

Answer:

 x=\frac{7}{6} and x =-2

Step-by-step explanation:

To solve for x, you must factor the equation first.

Factoring

6x^{2} +5x-14=0

*note - the constant number (14) is negative, which means that there must be a negative and a positive when factoring*

(6x - 7)(1x + 2)

When you multiply what is factored above, you get your original equation

Solving for x

As you may know, you will have two x answers.

(6x - 7) = 0 and (1x + 2) = 0

6x - 7 = 0 add 7 to both sides to get 6x alone

6x = 7 divide both sides by 6 to get x

x = 7/6

1x + 2 = 0 subtract 2 from both sides to get 1x alone

1x = -2 divide both sides by 1 to get x

x = -2

5 0
3 years ago
The surface area of 2 spheres are in ration of 1:16 what is the ratio of their volume
crimeas [40]
S1/S2 = 1/16
Thus R1/R2 = 1/4
So V1/V2 = 1/64
Answer: 1/64
4 0
3 years ago
You need 3 sticks of butter for every 24 cookies. If you have 5 sticks of butter how many cookies is that?
Ber [7]

Answer:

5:40

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
A skilled chess player believes that when they play a novice opponent, there is a 90% probability they will be able to beat them
zavuch27 [327]

Answer:

b) Binomial

c) Poisson

Step-by-step explanation:

The geometric distribution is the number of trials required to have r successes. The measures the number of sucesses(wins), not the number of trials required to win r games. So the geometric distribution does not apply.

For each match, there are only two possible outcomes, either the skilled player wins, or he does not. The probability of the skilled player winning a game is independent of other games. So the binomial distribution applies.

We can also find the expected number of wins of the skilled player, which is 15*0.9 = 13.5. The Poisson distribution is a discrete distribution in which the only parameter is the expected number of sucesses. So the Poisson distribution applies.

So the correct answer is:

b) Binomial

c) Poisson

7 0
4 years ago
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Sylvie and Bono hiked​
LUCKY_DIMON [66]

Answer:

Option C.

Step-by-step explanation:

In this excercise we have to rest the altitude where they hiked on the second place, to the one were they departed from, in order to know how much they hiked.

So we do:

6,288-3,288 = 3,000.

The correct option is option C.

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4 years ago
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