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erik [133]
3 years ago
13

Write a polynomial of least degree with rational coefficients and with the root -19-5 square root 2.

Mathematics
1 answer:
iogann1982 [59]3 years ago
5 0

Answer:

y = x² + 38x + 311

Step-by-step explanation:

If a polynomial has rational coefficients and irrational roots, then the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Use FOIL to distribute:

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

Use FOIL to distribute the last term:

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

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Please help me with a geometry problem, I don't understand.
Goshia [24]

The slope-intercept form:

y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

m - slope

b - y-intercept

We have the points (1, -5) and (9, 11). Substitute:

m=\dfrac{11-(-5)}{9-1}=\dfrac{16}{8}=2

Therefore we have

y=2x+b

Put the coordinates of the point (1, -5) to the equation:

-5=2(1)+b\\\\-5=2+b\qquad\text{subtract 2 from both sides}\\\\-7=b\to b=-7

<h3>Answer: y = 2x - 7</h3>
6 0
3 years ago
The cost of a circular table is directly proportional to the square of the radius. A circular table with a radius of 50cm costs
Lana71 [14]

Answer:

£135 is the correct answer.

Step-by-step explanation:

Let C be the cost of table.

And let R be the radius of table.

Cost of table is directly proportional to square of radius.

As per question statement:

C\propto R^{2} or

C=a\times R^2  ....... (1)

where a is the constant to remove the \propto sign.

It is given that

C_1 = £60 and R_1 = 50\ cm

C_2 = ? when R_2= 75\ cm

Putting the values of C_1 and R_1 in equation (1):

60=a \times 50^2  ....... (2)

Putting the values of C_2 and R_2 in equation (1):

C_2=a \times 75^2  ....... (3)

Dividing equation (2) by (3):

\dfrac{60}{C_2}= \dfrac{a \times 50^2}{a \times 75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{50^2}{75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{2^2}{3^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{4}{9}\\\Rightarrow C_2 = 15 \times 9 \\\Rightarrow C_2 = 135

So, <em>£135 is the correct answer</em>.

7 0
3 years ago
Find the complement of an angle that measures 3 degrees
Mnenie [13.5K]

Answer:

87

Step-by-step explanation:

Complementary angles add to 90 degrees

Let c be the complement

c + 3 = 90

Subtract 3 from each side

c+3-3 = 90-3

c = 87

6 0
4 years ago
simplify the following polynomial expression. <img src="https://tex.z-dn.net/?f=%285x%5E%7B3%7D%20%2B4x%5E%7B2%7D%20%2B6x-3%29%2
FrozenT [24]
Here is the answer hope it helps

7 0
4 years ago
The perimeter of a rectangle is 84cm . It's longest side is 29cm. State the length of the shortest side
Mumz [18]

Answer:

13cm

Step-by-step explanation:

29x2=58

84-58=26

26÷2=13

7 0
3 years ago
Read 2 more answers
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