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nadezda [96]
3 years ago
6

Find a degree 3 polynomial with real coefficients having zeros 1 and 2-2i and a lead coefficient of 1. Write P in expanded form.

Be sure to write the full equation, including P(x)=.
Mathematics
1 answer:
amm18123 years ago
4 0

Answer:

Step-by-step explanation:

complex roots always occur in pairs.

roots are 1,2-2i,2+2i

P(x)=a(x-a)(x-b)(x-c)

P(x)=1(x-1)[x-(2-2i)][x-(2+2i)]

=1(x-1)[(x-2)+2i][(x-2)-2i]

=(x-1)[(x-2)²-(2i)²]

=(x-1)[(x-2)²-4i²]

=(x-1)[x²-4x+4-4(-1)]

=(x-1)[x²-4x+4+4]

=(x-1)[x²-4x+8]

=x³-4x²+8x-x²+4x-8

=x³-5x²+12x-8

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Please work out and explain​
Mekhanik [1.2K]

Answer:

a = 22

b = 31

c = 13

Step-by-step explanation:

The sum is the same in each row, column, and diagonal.

One of the diagonals is already complete.  The sum is:

16 + 25 + 34 = 75

So the first row adds up to 75:

a + 37 + 16 = 75

a = 22

The second row adds up to 75:

19 + 25 + b = 75

b = 31

And the third row adds up to 75:

34 + c + 28 = 75

c = 13

We can check our answer by finding the sum of each column and the other diagonal.

22 + 19 + 34 = 75

37 + 25 + 13 = 75

16 + 31 + 28 = 75

22 + 25 + 28 = 75

3 0
3 years ago
Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45. If Alaina makes the purchase, which integer
valentina_108 [34]

Answer:

The Integer is -17

Step-by-step explanation:

This is because you must subtract the cost of the shoes from her account

28 - 45 is equal to negative 17

4 0
3 years ago
A boat is 60m from the base of a lighthouse. The angle of depression between the lighthouse and the boat is 37°. How tall is the
LekaFEV [45]

Answer: 34.64 m

Step-by-step explanation:

Given: A boat is 60 m from the base of a lighthouse.

The angle of depression between the lighthouse and the boat is 37°.

By using trigonometric ratios :

\tan x=\dfrac{\text{Side opposite to }x}{\text{Side adjacent to }x}

here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m

\tan 37^{\circ}=\dfrac{h}{60}\\\\\Rightarrow\ 0.57735=\dfrac{h}{60}\\\\\Rightarrow\ h= 60\times0.57735\approx34.64

Hence, the lighthouse is 34.64 m tall.

6 0
3 years ago
The difference of two numbers is 40. Their sum is 66. Find the numbers.
Margaret [11]
First of all, x>y
x-y=40
and
x+y=66
add them equations together to eliminate

x-y=40
<u>x+y=66 +</u>
2x+0y=106

2x=106
divide by 2
x=53

sub back
x-y=40
53-y=40
minus 53 both sides
-y=-13
y=13


the numbers are 53 and 13
8 0
3 years ago
Read 2 more answers
Refer to the article "Fire Up the Sun."
Dmitry [639]

Based on the information given, it should be noted the central idea is C. Making and using a solar oven is a learning experience.

<h3>What is a central idea?</h3>

A central idea simply means the main idea that's in a literary work. It's the unifying element that's in a story.

The central idea is that making and using a solar oven is a learning experience and the detail that supports the central idea is that "by completing this project, you will make an inexpensive, ecologically friendly piece of equipment and learn about the science behind what you’re doing".

Learn more about central ideas on:

brainly.com/question/2684713

8 0
2 years ago
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