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Genrish500 [490]
2 years ago
5

Find a polynomial F(x) of degree 3 with real coefficients and the following zeros. 4,1-i help fast please?

Mathematics
2 answers:
EastWind [94]2 years ago
8 0

Answer:

f(x) = x³ - 6x² + 10x - 8

Step-by-step explanation:

Complex zeros occur as conjugate pairs, thus

Given x = 1 - i is a zero then x = 1 + i is also a zero

Given the zeros are

x = 4, x = 1 - i, x = 1 + i then the corresponding factors are

(x - 4), (x - (1 - i) ), (x - (1 + i ) ), that is

(x + 4), ( x - 1 + i), (x - 1 - i)

f(x) is then the product of the factors, that is

f(x) = (x - 4)((x - 1) + i)((x - 1) - i ) ← distribute the complex factors

     = (x - 4)((x - 1)²  - i² ) → i² = - 1

     = (x - 4)(x² - 2x + 1 + 1)

     = (x - 4)(x² - 2x + 2) ← distribute

     = x³ - 2x² + 2x - 4x² + 8x - 8 ← collect like term

f(x) = x³ - 6x² + 10x - 8

Rus_ich [418]2 years ago
6 0

Answer:

f(x)=x3−x2−6x2+16x−10

Step-by-step explanation:

If 3−i is a zero, then 3+i

must be a zero as they are conjugates:

f( x ) = ( x − 1 ) ( x − ( 3 − i )) ( x − ( 3 + i )) f ( x ) = ( x − 1 ) ( x2 − x ( 3 + i ) − x ( 3 − i ) + 9 + 1 ) f ( x )) ( x − 1 ) ( x2 − 6x + 10 ) f ( x ) = x3 − x 2 − 6 x 2 + 16x − 10

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Lesson Posttest
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Answer:

1

Step-by-step explanation:

Probability = number of fruit type/total number of fruit. Total number of fruit = 5 + 9 + 5 = 19.

The probability of drawing an apple is P(apple) = number of apples/total number of fruit = 5/19.

The probability of drawing a peach is P(peach) = number of peaches/total number of fruit = 9/19

The probability of drawing an apple is P(orange) = number of oranges/total number of fruit = 5/19

The probability of drawing either an apple, peach or orange at the first draw of fruit from the bag is

P(apple or peach or orange) =  P(apple) + P(peach) + P(orange)

                                               = 5/19 + 9/19 + 5/19

                                               = (5 + 9 + 5)/19

                                               = 19/19

                                               = 1

3 0
3 years ago
The answer's are in the image sorry if you cant see them
Simora [160]
C. "David's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings"

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Hope this helps :)
8 0
3 years ago
What is ten times less than 700?
Ghella [55]
700/10 equals 70, so the answer is 70.
6 0
3 years ago
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Please help me with this​
stira [4]

Answer:

in the intersection region of all the solution in the system.

8 0
2 years ago
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mote1985 [20]

♡ The Question ♡

- Which of the following is equivalent to the power shown below? 8^4

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

☆ The Answer ☆

- Your answer should be C!

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Explanation/Step-By-Step ♡

- When your power is being shown as 8^4, this can be represented as 'Eight four times.' This means it could be, 8, 8, 8, 8. Hope this helps!

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

☆ Tips ☆

- No tips provided!

4 0
2 years ago
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