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Paha777 [63]
2 years ago
10

Find a polynomial function of degree 3 with 2, i, -i as zeros.

Mathematics
1 answer:
Simora [160]2 years ago
5 0

Answer:

p(x)= x^3-2x^2+x-2

Step-by-step explanation:

Here we are given that a polynomial has zeros as 2 , i and -i . We need to find out the cubic polynomial . In general we know that if \alpha , \ \beta \ \& \ \gamma are the zeros of the cubic polynomial , then ,

\sf \longrightarrow p(x)= (x -\alpha )(x-\beta)(x-\gamma)

Here in place of the Greek letters , substitute 2,i and -i , we get ,

\sf\longrightarrow p(x)= (x -2 )(x-i)(x+i)

Now multiply (x-i) and (x+i ) using the identity (a+b)(a-b)=a² - b² , we have ,

\sf  \longrightarrow p(x)= (x-2)\{ x^2 - (i)^2\}

Simplify using i = √-1 ,

\sf \longrightarrow p(x)= (x-2)( x^2 + 1 )

Multiply by distribution ,

\sf \longrightarrow p(x)= x(x^2+1) -2(x^2+1)

Simplify by opening the brackets ,

\sf\longrightarrow p(x)= x^3+x-2x^2-2

Rearrange ,

\sf\longrightarrow \underline{\boxed{\blue{\sf p(x)= x^3-2x^2+x-2}}}

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Solve for x and y:<br>x = <br>y = ​
ICE Princess25 [194]

Answer:

x = 15

y = 21

Step-by-step explanation:

*triangle sum theorem*

(6x - 11)° + (81)° + (x + 5)° = 180°

(7x - 6)° + (81)° = 180°

(7x)° + (75)° = 180°

(7x)° = (105)°

x = 15

________________

*vertical angle theorem* *triangle sum theorem*

(6x - 11)° + (4y - 18)° + (y + 14)° = 180°

^

|

15

(79°) + (4y + y) + (14 - 18)°

_________________________

(79)° + (5y - 4)° = 180°

(5y)° + (75)° = 180°

(5y)° = 105°

y = 21

5 0
3 years ago
Emily read 24 fiction books and 2 nonfiction books. What is the ratio of the number of fiction books she read to the total numbe
Tems11 [23]

The ratio of number of fiction books to total number of books that she read   12:13.

Given :

Emily reads 24 friction books and 2 nonfiction books.

Number of fiction books she read =24

Number of nofiction boos she read = 2

Total number of books = 26

To Find :

What is the ratio of the number of fiction books she read to the total number of books that she read ?

Solution :

Total number of books that she read=24+2=26

number of fiction books she read=24

Thus ratio of number of fiction books to total number of books that she read

 ⇒  \frac{24}{26}

 ⇒  \frac{12}{13}

 ⇒ 12: 13

Hence  ratio of number of fiction books to total number of books that she read 12 : 13

To know more about total number of books visit :

brainly.com/question/1179123

#SPJ1

4 0
1 year ago
Given that a triangle has two sides of lengths 5 inches and 7 inches, which is a possible length of the third side?
victus00 [196]

Answer:

big poop face looking butt with a massive forehead poopy duck dipers

Step-by-step explanation:

↑∴↔↔⇔⇔³∛÷≈≤≥≥β⇵⊕⊕¬⊕⊕⊕⊕⊕⊕¬∪∪⊥∡∠°∞㏒㏑∡Ф⇒⇒√³π∫↓∵∴∴\lim_{n \to \infty} a_n  \lim_{n \to \infty} a_n \neq \sqrt{x} x^{2} x^{2} \geq \geq \pi \frac{x}{y} and thats why it is big poop face looking butt with a massive forehead poopy duck dipers

3 0
3 years ago
Jared has a wooden board 11 ft long. He wants to cut it into two pieces so that the longer piece (y) is 4 ft less than 4 times t
patriot [66]

Answer:

the answer is x + y = 11 and y = 4x - 4

8 0
2 years ago
This is a number like 10 101,000 and so on it it is the result of using only a 10 as a factor
BaLLatris [955]

Answer: it is called the powers of ten

Step-by-step explanation:

7 0
3 years ago
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