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
Mashutka [201]
2 years ago
12

How do I use the Descartes Rule of Signs to determine all possible number of positive and negative zeros?

Mathematics
1 answer:
larisa [96]2 years ago
8 0

Answer:

We conclude that:

  • 2  or 0 positive real roots
  • 2  or 0 negative real roots

Step-by-step explanation:

Descartes Rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is:

  • Either equal to the number of sign differences between consecutive nonzero coefficients,
  • Or is less than it by an even number.

Given the function

f\left(x\right)=x^4-2x^3-4x^2+2x+3

So, the coefficients are 1, −2, −4, 2, 3

As can be seen, there are 2 changes.

This means that there are 2 or 0 positive real roots.

To find the number of negative real roots, substitute x with -x in the given polynomial:

x^4-2x^3-4x^2+2x+3  becomes x^4+2x^3-4x^2-2x+3

The coefficients are 1, 2, −4, −2, 3

As can be seen, there are 2 changes.

This means that there are 2 or 0 negative real roots.

Therefore, we conclude that:

  • 2  or 0 positive real roots
  • 2  or 0 negative real roots

You might be interested in
from the set {-512,-8,8} ,use substitution to determine which value of x makes the equation true -64x=-1,152
Llana [10]

Answer:

18

Step-by-step explanation:

Just divide both sides by - 64

6 0
3 years ago
Find k so that the following function is continuous:<br> f(x)={kx8x2if0≤x&lt;5if5≤x.
tankabanditka [31]

Check the one-sided limits:

\displaystyle \lim_{x\to5^-}f(x) = \lim_{x\to5}kx = 5k

\displaystyle \lim_{x\to5^+}f(x) = \lim_{x\to5}8x^2 = 200

If <em>f(x)</em> is to be continuous at <em>x</em> = 5, then these two limits should have the same value, which means

5<em>k</em> = 200

<em>k</em> = 200/5

<em>k</em> = 40

3 0
2 years ago
Which of the following fractions is equivalent to -84/-90 in the least common terms?
abruzzese [7]
Answer: 14/15

This is because to get to 14/15 you must divide by 6 but when getting to 42/45 you must divide 2. Therefore 14/15 is your answer because the problem went to the most reduced fraction.
5 0
3 years ago
suppose you could climb to the top of the pyramid arena in memphis tennessee. which path would be shorter, climbing a lateral ed
olga_2 [115]
I would say the slant height
4 0
3 years ago
Square root 1.96? is rational irrational
Kruka [31]

Answer:

Rational

Step-by-step explanation:

An irrational number is a number with forever continuing decimals. Plug it into the calc and you can see if there is a long decimal line that ends. You should get 1.4 in the calc, and since it does end, it is a rational number.

4 0
3 years ago
Other questions:
  • I need help with this ....!!!!!
    11·1 answer
  • What is the maximum height of the basketball when the player passes the ball to someone? Initially, the ball moves at a speed of
    6·1 answer
  • Given the function ƒ(x )=x^2 - 5, find ƒ(7).<br><br> 49 <br><br> 2 <br><br> 44
    15·2 answers
  • 13/7=u/4 <br> Solve for u please
    13·1 answer
  • Determine the zeros of the function f(x) = 332 – 7x + 1.
    8·1 answer
  • What is 3/9 in its lowest terms?
    12·2 answers
  • Please hurry!! Which statement is true regarding the functions
    11·1 answer
  • Every day Michelle does four more high jumps than Cintia. Which of the following graphs correctly represents the relationship be
    7·1 answer
  • 15 more than the quotient of a number x and 12.
    6·1 answer
  • Suppose f(x)=x+3 find the graph of f(2x)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!