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klio [65]
3 years ago
9

What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?

Mathematics
2 answers:
Helga [31]3 years ago
5 0

Answer:

f(x) = x3 – 3x2 + 4x – 2

Step-by-step explanation:

astra-53 [7]3 years ago
4 0

x³ - 3x² + 4x - 2

complex roots occur in conjugate pairs

1 + i is a root then so is 1 - i

the factors of the polynomial are therefore

f(x) = (x - 1 )(x - (1 + i))(x - (1 - i))

     = (x - 1 )(x² - 2x + 2 ) ( expand factors and simplify )

     = x³ - 3x² + 4x - 2



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In Store A, you can buy 3 notebooks
PolarNik [594]

Answer:

The price of one notebook is 2$

Step-by-step explanation:

3x + 2= 4x

Take x to the same side —> 4x-3x=2 —> x=2

3 0
3 years ago
You can jog around the block twice and the park once in 10 min. You can jog around the block twice and the park 3 times in 22 mi
stich3 [128]
B = block     p = park

2b + p = 10 min                2 runs around the block takes 10 minutes
2b + 3p = 22 min        2 runs around the block plus 3 runs around the park                                                       takes 22 minutes

To solve, I will use substitution. First, I will divide the first equation by 2 to get b by itself and subtract p from both sides to get b by itself. Then, substitute 5 - 1/2p in for b in the second equation because they have equal values. Then, subtract 10 from both sides to eliminate it. Divide by 2 to both sides to get 'p' by itself.

2b + p = 10 min ---------→b + 1/2p = 5 ----------→ b = 5 - 1/2p

2(5 - 1/2p) + 3p = 22 ---------→ 10 -p + 3p = 22 --------→ 10 + 2p = 22

10 + 3p = 22 ----------→ 2p = 12

2p = 12 -------------→ p = 6

It takes 6 minutes to jog around the park

Hope this helps!
6 0
3 years ago
Desmond paid 8.5% sales tax when he bought a new phone. The sales tax was $12.75. What was the cost of the phone, without tax? *
Over [174]

Answer: 150$

Step-by-step explanation:

12.75 / 8.5%

6 0
3 years ago
The larger of two consecutive integers is 7 greater than twice the smaller. Find the integers.
belka [17]

Answer:

8,9

Step-by-step explanation:

(x +1) + 7=2x

x+8 = 2x

8=x

4 0
3 years ago
Determine which equations below, when combined with the equation 3x minus 4y equals 2, will form a system with no solutions. cho
kirill115 [55]
The two equations would yield no solution if they are dependent. That means that both equations are equivalent. You can determine this by manipulating the equations through simplification. For example, a dependent equation would be:

3x - 4y = 2
3x/2 - 2y = 1

Another dependent equation is when you multiply the whole equation with a number, say 3.
(3x - 4y = 2)3
9x - 12y = 6
8 0
3 years ago
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