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aliina [53]
2 years ago
7

If a polynomial has one root in the form a+√b , it has a second root in the form of a_√b

Mathematics
2 answers:
Naily [24]2 years ago
8 0

Answer:

Step-by-step explanation:the answer is a minus sign

gulaghasi [49]2 years ago
3 0
When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.

The first factor is x - (a + √b).
The second factor is x - (a - √b).

The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
      = x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
      = x² - 2ax + x√b - x√b + a² - b
      = x² - 2ax + a² - b

This is a quadratic polynomial, as expected.

If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
   = a +/- (1/2)*√(4b)
   = a +/- √b
x = a + √b, or x = a - √b, as expected.
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A contractor has been hired to install flooring for a bandstand in the shape of a circle that is 21 feet across. How many square
SOVA2 [1]

Answer:

A. 346.19 square feet.

Step-by-step explanation:

We have been given that a contractor has been hired to install flooring for a bandstand in the shape of a circle that is 21 feet across.

To find the square feet of flooring required, we will find area of circle.

Since the length across the circle is 21 feet, so radius of circle will be half of 21 feet.

\text{Radius}=\frac{\text{21 feet}}{2}

\text{Radius}=\text{10.5 feet}

\text{Area of circle}=\pi r^2

\text{Area of circle}=\pi (\text{10.5 feet})^2

\text{Area of circle}=3.14*110.25\text{ feet}^2

\text{Area of circle}=346.185\text{ feet}^2

\text{Area of circle}\approx 346.19\text{ feet}^2

Therefore, 346.19 square feet of flooring will be required.

3 0
3 years ago
Read 2 more answers
99.7 of all newborn babies in the United States weigh between
Marina CMI [18]

Answer:

2000-5000 g

Step-by-step explanation:

Averagely, the weight of a new born baby is 7.5 lb, which is equal to 3.5 kg.

Converting this weight in kg to grams,

3.5 kg = 3.5 *1000 = 3500 g

From the answer choices, the value will range from 2000 g-5000 g

4 0
3 years ago
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Find the solution to the following system using substitution or elimination:​
raketka [301]

Answer:

B) (3,1)

Step-by-step explanation:

y = -2x + 7

y = 3x - 8

3x - 8 = -2x + 7

combine like terms:

5x = 15

divide both sides of the equation by 5:

x = 3

y = 3(3) - 8 = 1

4 0
3 years ago
Given a quadratic function in vertex form:
Alja [10]

Answer:

See below

Step-by-step explanation:

<u>Part A</u>

A vertical stretch takes place when a\cdot f(x) given that  |a| > 1

<u>Part B</u>

A vertical compression takes place when a\cdot f(x) given that 0 < |a| < 1

<u>Part C</u>

A vertical stretch is different than a horizontal compression:

  • In a vertical stretch, the input stays the same, but the output is multiplied by the scale factor
  • In a horizontal compression, the output stays the same, but the input is multiplied by the scale factor

<u>Part D</u>

A reflection across the x-axis means that the output, our y-variable, is the opposite sign. This means that all values of a must be negative such that a\cdot f(x) as mentioned in parts A and B. Also, in part C, since our scale factor is negative, the output is the only one being multiplied by the scale factor.

7 0
2 years ago
Which of the following expressions has the greatest value?
Vilka [71]

Answer:

2^5

Step-by-step explanation:

1^10 = 1 (1*1*1*1*1....)

5^2 = 25 (5*5)

2^5 = 32 (2*2*2*2*2)

3^3 = 27 (3*3*3)

5 0
3 years ago
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