1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timama [110]
3 years ago
5

Write a polynomial function of least degree with the given zero. -1+ √ 2, √ 3

Mathematics
1 answer:
kirill115 [55]3 years ago
6 0

Answer:

f(x) = x^{4} + 2x³ - 4x² - 6x + 3

Step-by-step explanation:

Note that radical zeros occur in conjugate pairs, thus

- 1 + \sqrt{2} is a zero then - 1 - \sqrt{2} is also a zero

\sqrt{3} is a zero then - \sqrt{3} is also a zero

Thus the corresponding factors are

(x - (- 1 + \sqrt{2}) ), (x - (- 1 - \sqrt{2}) ), (x - \sqrt{3}), (x - (- \sqrt{3})), that is

(x + 1 - \sqrt{2}), (x + 1 + \sqrt{2}), (x - \sqrt{3}), (x + \sqrt{3})

The polynomial is then the product of the roots

f(x) = (x + 1 - \sqrt{2})(x + 1 + \sqrt{2})(x - \sqrt{3})(x + \sqrt{3})

     = ((x + 1)² - (\sqrt{2})²)((x² - (\sqrt{3})²)

     = (x² + 2x + 1 - 2)(x² - 3)

     = (x² + 2x - 1)(x² - 3) ← distribute

     = x^{4} - 3x² + 2x³ - 6x - x² + 3

     = x^{4} + 2x³ - 4x² - 6x + 3

You might be interested in
If 5 times a number is subtracted from 3 times its<br>square, the result is 2. Find the number.​
grandymaker [24]

Answer:

x = 2 or x = - 1/3

Step-by-step explanation:

3x² - 5x = 2

3x² - 5x - 2 = 0

(x - 2) (3x + 1) = 0

x = 2 or x = - 1/3

5 0
3 years ago
FIND THE EXACT AREA OF THE SHADED <br> PLEASE HELP ILL GIVE BRAINLIESTTTTTT
astra-53 [7]
1)
area of half of the circle: 628.32
are of parallelogram: 4000
Exact area of shaded: 3,371.68 cm squared.
The answer to the equation under the shape is: A = 4000 - 628.32 π in²

2)
area of both circles added together: 173.18
full area of rectangle: 220.5
Exact area of shaded: 47.32
The answer to the equation under the shape is: A = 220.5 - 173.18 π in²

Hope this helps!
Please give Brainliest!
8 0
1 year ago
Emily, Jean, and Amanda live in apartments on the 5th, 6th and 7th floors. One girl likes basketball, one likes football, and th
ss7ja [257]

Answer:

Assuming you mean baseball in stead of basketball, if must be the 5th floor.

Step-by-step explanation:

"The girl on the fifth floor thinks soccer is boring" implies that on the 5th floor lives the football or baseball fan. However, it cannot be the football fan since it is already known that she lives on 6th.

So the baseball fan, which is Jean, lives on 5th.

3 0
3 years ago
What is 9 2/3 - 2 8/10
umka21 [38]
9 2/3 - 2 8/10 = 16 13/15
7 0
3 years ago
3. A bicycle wheel has a diameter of 559 mm and has 32 equally spaced spokes. What is the approximate arc
bija089 [108]
Circumference = πd = 3.14*559 = 1755.26
The spokes divide the circumference into 32 arcs. Each arc length is 1755.26/32 = 54.75 mm
4 0
3 years ago
Other questions:
  • Expression equivalent to 3(2t + 6 )-4t
    11·1 answer
  • Adding 7 to q number is the same as subracting 4 from double the number, what is the number?​
    13·1 answer
  • Three added to 4 times a number is equal to 5 less than 6 times the number.
    14·1 answer
  • 53 freshman were interviewed about the classes they were taking this semester 24 said they were taking science 22 said they were
    11·1 answer
  • Isabelle is mixing red paint with blue paint to make purple paint. She adds 3/10 of a fluid ounce of red to 11/15 of a fluid oun
    12·2 answers
  • Please help with this question
    11·2 answers
  • Simplify the expression (2/9) ^2
    14·1 answer
  • Four teachers share 3 gallons of paint equally. How much paint does each teacher get
    11·2 answers
  • What’s this someone answer 15 points
    7·1 answer
  • Fide the volume and round to the nearest tenth I will give brainless
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!