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
Lady bird [3.3K]
2 years ago
15

what is the polynomial function of lowest degree with leading coefficient of 1 and roots 2 and 1 + square root2

Mathematics
1 answer:
Marta_Voda [28]2 years ago
5 0
If the roots to such a polynomial are 2 and 1+\sqrt2, then we can write it as

(x-2)(x-(1+\sqrt2))

courtesy of the fundamental theorem of algebra. Now expanding yields

(x-2)(x-1-\sqrt2)=x^2-2x-(1+\sqrt2)x+2(1+\sqrt2)=x^2-(3+\sqrt2)x+2+2\sqrt2

which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.

So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use 1-\sqrt2 as a root. In this case, that would make our polynomial

(x-2)(x-(1+\sqrt2))(x-(1-\sqrt2))=x^3-4x^2+3x+2

so that the answer is (probably) the third choice.

Whoever originally wrote this question should reevaluate their word choice...
You might be interested in
How to answer h/4 ≤ 2/7
Serjik [45]

I feel you, headaches suck.

Your answer would be  h ≤ 8/7

Step  1  :

           2

Simplify   —

           7

Equation at the end of step  1  :

 h    2

 — -  —  ≤ 0

 4    7

Step  2  :

           h

Simplify   —

           4

Equation at the end of step  2  :

 h    2

 — -  —  ≤ 0

 4    7

Step  3  :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       4

     The right denominator is :       7

After calculating the multipliers you get  h ≤ 8/7

Hope this helps!

Please consider Brainliest!

4 0
3 years ago
The questions and answers are in the picture. Will give brainliest!
mariarad [96]

Answer:

Image D is correct.

5 0
3 years ago
Read 2 more answers
What is the description of the translation from f(x)=9x+3 to g(x)=4x+3?
Assoli18 [71]
I’m pretty sure- B) counterclockwise rotation
-
-

5 0
3 years ago
On a loan of $1200 at 15% annual interest, Shirley had to pay $135 interest. For how many months did she have the loan?
natulia [17]

Answer:

<u><em>9 months</em></u>

Step-by-step explanation:

Principal= P= $1200

Rate=R= 15%

Interest= I= $135

Time= T= ?

I=P*R*T/100

135= 1200*15*T/100

135*100=18000*T

13500/18000=T

T= 0.75 years

T= 0.75*12= 9 months

3 0
2 years ago
Read 2 more answers
Daniel has a coupon for $1.44 off
Art [367]

Answer:

Daniel will save $1.18

Step-by-step explanation:

First, find the cost of the name-brand flour with the coupon:

Subtract 1.44 from the original price of 9.12:

9.12 - 1.44

= 7.68

So, the price of the name-brand flour with the coupon is $7.68

Now, find how much he will save by finding the difference between this price and the price of the store brand flour:

8.86 - 7.68

= 1.18

So, Daniel will save $1.18

3 0
2 years ago
Other questions:
  • 5.6<br> c<br> -<br> 7.2<br> &lt;<br> -<br> 15.6
    15·1 answer
  • Which polynomial is in standard form
    13·1 answer
  • Which one is higher 45 fahrenheit or 30 celsius?
    8·1 answer
  • to mix a punch, Lindsay begins with 3 liters of lemon lime soda and adds 1,893 millilters of cranberry juice. How many liters ar
    13·2 answers
  • 10. For f(x) = 3 - 5x, find f(-5).<br> A. –22<br> B. -7<br> C. 3<br> D. 28
    6·1 answer
  • For 100​ births, P(exactly 55 ​girls)equals0.0485 and ​P(55 or more ​girls)equals0.184. Is 55 girls in 100 births a significantl
    15·1 answer
  • HELP ASAP!!!! 10 PTS<br> What is the value of m? 0.61m−1.51m=9
    10·2 answers
  • Gemma and Leah are both jewelry maker Gemma 106 beaded necklaces Leah made 39 more necklaces then Gemma
    5·1 answer
  • 4x + y = -1<br> 4x - 3y = 7<br> Solve the simultaneous equation.<br><br> x=__<br> y=__
    9·1 answer
  • Year to date revenue
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!