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
Sav [38]
3 years ago
6

1. While solutions to the general quintic equation in terms of radicals are impossible to obtain, they do exist. Prove that the

given quintic equation has real solutions. x^5-3x+1=0
Mathematics
2 answers:
xenn [34]3 years ago
8 0

Answer with step-by-step explanation:

Quintic function :It is defined as the function of degree five.

It can be defined ax^5+bx^4+cx^3+dx^2+ex+f=0

Wherea\neq0,b,c,d,e and f are members of field , typically rational numbers,real numbers and complex numbers .

We are given that quintic equation

x^5-3x+1=0

We have to prove that given quintic equation has real solutions

Using Discarte's rule

f(x)=x^5-3x+1

When are going from coefficient of first term to coefficient of second term then sign change and when we are going from coefficient of second term to coefficient of third term then sigh also changes .Therefore,, there are two times sign change .Hence, possible positive real roots are 2 or zero.Then number of positive real roots are even in number .

f(-x)=-x^5+3x+1

When we are going from first term to second term then sign change and then from second term to third term then sign does not changes.

Hence, possible negative real root is   1.

Therefore, we can say given quintic equation has real root.

Hence, proved

Marta_Voda [28]3 years ago
3 0

Answer:

Step-by-step explanation:

Given is a function as x^5-3x+1

Equating to 0 we have equation

If the function f(x) has x intercepts then the solutions are real

Let us use remainder theorem and change of signs rule

f(0) = 1>0

f(-1) = -1+3+1=3

f(-2) = -32+6+1<0

This implies there is a real root between -1 and -2.

f(1) = -1

Since f(0) and f(1) have different signs, there exists a real root between 0 and 1.

f(2) = 32-6+1>0

Since f(1) and f(2) have different signs there exists a real root between 1 and 2.

Thus there are definitely three real solutions as

one between -1 and 0, one between 0 and 1, and third between 1 and 2.

You might be interested in
Solve the following system of equations:<br> x − 2y = 5<br> 2x − 4y = 10
Pie
These equation have <span>Infinitely Many Solutions.

I hope this helps.

Have a awesome day. :)</span>
7 0
2 years ago
Read 2 more answers
How would you solve the equation 4× =100​
gogolik [260]

Answer:

divide both sides by 4

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Type an equivalent expression to show the relationship of multiplication and addition<br> 7+7+7+7+7
nikitadnepr [17]
7 • 5



Multiplication is basically repeated addition. So to convert repeated addition to multiplication, we take the number being added (7) and multiply it be the number of addens (5). Therefore, 7+7+7+7+7 = 5 • 7
3 0
3 years ago
Help!
Olin [163]

Answer:

2/16

1/8

Step-by-step explanation:

8/1=8

2/16=0.125 which is equal to 1/8

2/14=1/7

1/8=1/8 is 2/16 simplified so they are the same

14/2=7

6 0
2 years ago
E<br> B<br> 30<br> 24<br> 25<br> 20<br> А<br> 15<br> с<br> D<br> 18<br> F<br> The scale factor is
Finger [1]

Answer:

5:6

Step-by-step explanation:

20/4=5

24/4=6

20:24 ratio simplified is 5:6

sorry if wrong

3 0
2 years ago
Other questions:
  • A publisher pays 6% royalty to a book writer for the first 1,000 copies sold, and 5% on any number of copies above 1,000. They w
    11·1 answer
  • Compare. the values and order them from least to greatest. 3.65 feet 4.1 feet 3 11/16 feet
    15·1 answer
  • What is the numerator when 0.83 is written as a fraction with a denominator of 100
    7·1 answer
  • What is the domain of the given function?
    9·1 answer
  • Y 2 + 5y Choose the constant term that completes the perfect square trinomial.
    5·1 answer
  • Write in point-slope form an equation of the line that passes through the point (6,−1) with slope −1/3.
    6·2 answers
  • Help if you can plzz will mark you brainliest
    15·1 answer
  • Let A={1'3'5'6}<br> B={0'7}<br> check whether A and B are disjoint sets
    14·1 answer
  • Do y’all know the answer for 2/3+1/6q=5/6q+1/3
    5·1 answer
  • Sketch the region of integration and change the order of integration. $\int_{0}^{{\color{red}16}} \int_{0}^{\sqrt{x}} f(x, y)dy
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!