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yarga [219]
3 years ago
5

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

rm. Be sure to write the full equation, including P ( x ) = .
Mathematics
1 answer:
Zanzabum3 years ago
6 0

Answer:

The polynomial with real coefficients having zeros 2 and 2 - 2i is

x³ - 6x² + 16x - 16 = 0

Step-by-step explanation:

Given that a polynomial has zeros at 2 and 2 - 2i, we want to write this polynomial.

We have

x - 2 = 0

x - (2 - 2i) = 0

=> x - 2 + 2i = 0

Since the polynomial has real coefficients, and 2 - 2i is a zero of the polynomial, the conjugate of 2 - 2i, which is 2 + 2i is also a polynomial.

x - (2 + 2i) = 0

=> x - 2 - 2i = 0

Now,

P(x) = (x - 2)(x - 2 + 2i)(x - 2 - 2i) = 0

= (x - 2)((x - 2)² - (2i)²) = 0

= (x - 2)(x² - 4x + 8) = 0

= x³ - 4x² + 8x - 2x² + 8x - 16 = 0

= x³ - 6x² + 16x - 16 = 0

This is the polynomial required.

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3 years ago
A country will produce 3000 missiles this year. Each of the short-range missiles cost $200000 to produce. Each of the medium-ran
Lynna [10]

Answer:

$350,000

Step-by-step explanation:

Let's define:

  • s: amount of short-range missiles produced
  • m: amount of medium-range missiles produced
  • l: amount of long-range missiles produced

From the total production and the ratios we can write the following equations:

s + m + l = 3000

s/m = 3/3 = 1 = m/s

s/l = 3/4 or l/s = 4/3

Dividing the first equation by s, we get:

s/s + m/s + l/s = 3000/s

1 + 1 + 4/3 = 3000/s

10/3 = 3000/s

s = 3000*3/10 = 900

m = 900

l =  4/3*900 = 1200

From the money that the countries plans to use and each missile cost, we can write the following equation:

200,000*s + 300,000*m + cost*l = 870,000,000

Replacing with previous result:

200,000*900 + 300,000*900 + cost*1200 = 870,000,000

cost = (870,000,000 - 200,000*900 - 300,000*900)/1200 = 350,000

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3 years ago
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Stolb23 [73]

Answer:

The answer is 40.

Step-by-step explanation:

4x5 for the square part.

2x10 for the rectangle part

add them

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3 years ago
Read 2 more answers
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