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slamgirl [31]
3 years ago
11

N=4; 2i and 3i are zeros f(-1)=50

Mathematics
1 answer:
Nonamiya [84]3 years ago
6 0

Solution:- \text{Let f(x) be any nth degree polynomial with n=4}\\

\text{Given that 2i and 3i are the zeroes of f(x)}

\text{so (x-2i) and (x-3i) are factors of f(x)}

\text{Since 2i is a zero of f(x) then its conjugate -2i is also a zero of f(x)}

\Rightarrow(x+2i) \text{is a factor}\\\text{Similarly, conjugate of 3i is -3i is also a zero of f(x) }\\\Rightarrow(x+3i)\text{is a factor}\\\text{So , }\\f(x)=k(x-2i)(x+2i)(x-3i)(x+3i)\\=k(x^2-(2i)^2)(x^2-(3i)^2)\\=k(x^2-4i^2)(x^2-9i^2)\\=k(x^2+4)(x^2+9)\\=k(x^4+13x^2+36)\\\text{As given}\\f(-1)=50\\\Rightarrow k((-1)^4+13(-1)^2+36)=50\\\Rightarrow k(1+13+36)=50\\\Rightarrow k(50)=50\\\Rightarrow k=1\\\text{So by substituting k=1 in f(x) we get ,}\\f(x)=(x^4+13x^2+36)

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Karen has $1.70 in coins. Karen has 8 coins, all of which are quarters or dimes.
kumpel [21]

x+y=8 and 25x+10y=170 are the linear equations.

x+y≤8 and 25x+10y≤170 are the inequalities.

Step-by-step explanation:

Given,

Worth of coins = $1.70 = 1.70*100 = 170 cents

Number of coins = 8

1 quarter = 25 cents

1 dime = 10 cents

Let,

x represent the number of quarters

y represent the number of dimes

1. Write an equation to represent the amount of coins Karen has.

x+y = 8

2.Write an equation to represent the value of the coins Karen has.

25x+10y=170

x+y=8 and 25x+10y=170 are the linear equations.

For inequalities, the amount cannot increase number of coins and worth but it can be less, therefore,

x+y≤8

25x+10y≤170

x+y≤8 and 25x+10y≤170 are the inequalities.

Keywords: linear equations, addition

Learn more about linear equations at:

  • brainly.com/question/10570041
  • brainly.com/question/10610299

#LearnwithBrainly

4 0
3 years ago
For which real numbers x and y is it true that x + y = x+y?
Alchen [17]
By the general application of cumulative property of addition :

x + y = y + x

For sure
6 0
3 years ago
100<br> 200<br> 300<br> 400 500 600 700<br> Quantity Supplied<br> nstructions: Refer to the graph and answer the questions below
mash [69]

Answer:

a. 400

b. 4$

Step-by-step explanation:

2$ equals 0 Quantity

3$ equals 100 Quantity

4$ equals 200 Quantity

We can see that starting from 2$, a dollar will increase the Quantity by 100

7 0
1 year ago
If 3t -7 = 5t, then 6t =
USPshnik [31]

Answer:

21

Step-by-step explanation:

3t-7=5t

subtract 3t from both sides

-7 = 2t

multiply both sides by 3

-21 = 6t

so 6t = -21

5 0
1 year ago
Read 2 more answers
Simplify:
Mashutka [201]

Answer:

The answer is letter B.

Hope it will help you

4 0
3 years ago
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