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
kkurt [141]
3 years ago
14

Why is it remarkable that with real coefficients, there must be complex solutions?

Mathematics
1 answer:
kompoz [17]3 years ago
8 0

Answer:

it is important to learn about complex solution because polynomial equation formed over a complex number can only be solved by a complex number.

this is so because, the fundamental theorem of algebra state that every polynomial equation in one variable with complex coefficient has at least one complex solution.

Step-by-step explanation:

it is important to learn about complex solution because polynomial equation formed over a complex number can only be solved by a complex number.

this is so because, the fundamental theorem of algebra state that every polynomial equation in one variable with complex coefficient has at least one complex solution.

for example:

Given any positive integer n ≥ 1 and any choice of complex numbers a0,a1,...,an, such that an 6= 0,

the polynomial equation

anzn +···+ a1z + a0 = 0 (1) has at least one solution z ∈C.

No analogous result holds for guaranteeing that a real solution exists to Equation (1) if we restrict the coefficients a0,a1,...,an to be real numbers.

E.g., there does not exist a real number x satisfying an equation as simple as x2 + 1 = 0. Similarly, the consideration of polynomial equations having integer (resp. rational) coefficients quickly forces us to consider solutions that cannot possibly be integers (resp. rational numbers).

You might be interested in
Gloria sold 78 apples, Berta sold 4 less than 9 times as many apples as Gloria. How many apples did Berta Sell?
slega [8]

Answer:

698 apples

Step-by-step explanation:  78*9 equals 702.  She sold 4 less than that so you need to subtract 4.  702-4=698 apples Berta sold.

5 0
3 years ago
Urgent Please Help!!
Alenkinab [10]
I believe it’s X = 4

So 4 would be the answer
5 0
3 years ago
HELP QUICK PLEASE 15 points!!!
Reil [10]

Answer:

I think the ans is option 'a'

Final Answer:

Corresponding Angles Theorum; ∠AGF and ∠EHD are congruent

3 0
2 years ago
Simplify 3^-3<br> Show work
dmitriy555 [2]

\bf a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 3^{-3}\implies \cfrac{1}{3^3}\implies \cfrac{1}{27}

5 0
3 years ago
Factor each expression 8 16 =
dalvyx [7]
Since they are just next to each other ill take it multiplication and that would be 128 if its not let me know and ill correct it 
8 0
3 years ago
Other questions:
  • Thirty-five girls out of 100 play a musical instrument.what percentage of the girls do not play a musical instrument?
    12·2 answers
  • If Jerry Adams would normally pay $875 for bodily injury
    11·1 answer
  • What is true about the number 3.872? Check all that apply.
    8·2 answers
  • A rock is dropped from a height of 25 feet. The function h=-16t^2 +25 gives the height h of the rock after t seconds. When does
    14·1 answer
  • Help write them in standard form 20points do all
    14·1 answer
  • Listed are 32 ages for Academy Award winning best actors in order from smallest to largest. (Round your answers to the nearest w
    15·1 answer
  • Violet buys a premium sound system that is on sale for 40% off the original price. The original price is $224 more than the sale
    8·1 answer
  • In an arithmetic sequence, the 10th term is 37, and the 21st term is 4. Find the common difference and the first term
    9·1 answer
  • I have like 20 minutes please help<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D-7x%2B10%3D0" id="TexFormula1" title="x^{2}-7x+10
    14·1 answer
  • Gretchen earns seven dollars per hour at the local pizza shop if she works three hours in afternoon how much money does she earn
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!