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cricket20 [7]
3 years ago
8

The line plot shows the number of points scored by Josh in his basketball games. How many games did Josh score less than four po

ints? A) 10 B) 11 C) 12 D) 23
Mathematics
1 answer:
-Dominant- [34]3 years ago
5 0

Answer:

Step-by-step explanation:

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What are the types of roots of the equation below?<br> - 81=0
Tju [1.3M]

Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0. This can be obtained by finding root of the equation using algebraic identity.    

<h3>What are the types of roots of the equation below?</h3>

Here in the question it is given that,

  • the equation x⁴ - 81 = 0

By using algebraic identity, (a + b)(a - b) = a² - b², we get,  

⇒ x⁴ - 81 = 0                      

⇒ (x² +  9)(x² - 9) = 0

⇒ (x² + 9)(x² - 9) = 0

  1. (x² -  9) = (x² - 3²) = (x - 3)(x + 3) [using algebraic identity, (a + b)(a - b) = a² - b²]
  2. x² + 9 = 0 ⇒ x² = -9 ⇒ x = √-9 ⇒ x= √-1√9 ⇒x = ± 3i

⇒ (x² + 9) = (x - 3i)(x + 3i)

Now the equation becomes,

[(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

Therefore x + 3, x - 3, x + 3i and x - 3i are the roots of the equation

To check whether the roots are correct multiply the roots with each other,

⇒ [(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

⇒ [x² - 3x + 3x - 9][x² - 3xi + 3xi - 9i²] = 0

⇒ (x² +0x - 9)(x² +0xi - 9(- 1)) = 0

⇒ (x² - 9)(x² + 9) = 0

⇒ x⁴ - 9x² + 9x² - 81 = 0

⇒ x⁴ - 81 = 0

Hence Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: What are the types of roots of the equation below?

x⁴ - 81 = 0

A) Four Complex

B) Two Complex and Two Real

C) Four Real

Learn more about roots of equation here:

brainly.com/question/26926523

#SPJ9

5 0
1 year ago
The area of a square dollhouse is 289 square inches. How long is each side of the dollhouse?
EastWind [94]

Answer:

17

Step-by-step explanation:

8 0
3 years ago
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Hi, Guys This is Math 5th Grade I was Doing my homeWork when I did not know a question and I decided maybe 1 of you guys can hel
alexgriva [62]

Answer:

Circle A's attributes were used to be organized because both shapes have a <u>right angle</u>. Circle B's attributes were used to be organized because both shapes have <u>2 sets of parallel lines</u> that are across from each other. The middle was organized because both shapes have <u>2 sets of parallel lines</u> and <u>4 right angles</u>.

Step-by-step explanation:

Let me know if this helps!

6 0
2 years ago
What is the value of x
bulgar [2K]

x equals negative 8 that's it

5 0
3 years ago
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|5x|-2=18 helps love this problem please help
drek231 [11]

Answer:

x = 4

Step-by-step explanation:

The absolute value of 5x is still 5x.

5x - 2 = 18

Add 2 to both sides

5x = 20

Divide both sides by 5

x = 4

7 0
3 years ago
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