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antoniya [11.8K]
2 years ago
6

HELP PLEASE ANSWER THIS THANK YOU

Mathematics
1 answer:
vaieri [72.5K]2 years ago
3 0
6 just Count the pairs of 2
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Describe how both the Rational Root Theorem and Descartes’ Rules of Signs help you to find the zeros of a polynomial? Give me an
MrRa [10]

Answer:

Step-by-step explanation:

Rational Root Theorem: If the polynomial

P(x) = a n x n + a n – 1 x n – 1 + ... + a 2 x 2 + a 1 x + a 0

has any rational roots, then they must be of the form of (factors of a0/factors of an).

Example: F(x) = 4x² + 5x +2

If this polynomial has any rational roots, then they must be (factors of 2)/(factors of 4), so (±1, ±2)/(±1, ±2, ±4). So if this polynomial has any rational roots, they must be either: ±1, ±1/2, ±1/4, or ±2. Notice that this polynomial doesn't have to have any rational roots, but if it does, then the roots must fit the Rational Root Theorem.

Descartes' Rules of Signs:

a). In a polynomial, how many time the sign changes is how many positive roots the polynomial will have.

Example: 5x³ + 6x² - 2x - 1

In this expression, the sign only changed once, between 6x² and 2x, so it will only have one positive root.

Example 2: 6x³ - 4x² + x - 6

In this expression, the sign changed 3 times (remember there is a invisible "+" sign before the 6x³), so it will have 3 positive roots.

b). In a polynomial, if you plug in "-x" for all "x", then how many times the new polynomial changes sign is how many negative roots the old polynomial have.

Example: 5x³ + 6x² - 2x - 1.

If we plug in "-x" for all "x", then we get 5(-x)³ + 6(-x)² - 2(-x) -1, which simplifies to -5x³ + 6x² + 2x -1. In this new expression, the sign changed twice, so we have two negative roots for the expression. Notice how we got one positive root the first time and two negative roots the second time, and 1 + 2 = 3. The Fundamental Theorem of Algebra states that for a nth degree polynomial, it will have n complex roots. The polynomial we worked with was a 3rd degree polynomial, and we got 1 + 2 = 3 roots in the end.

4 0
3 years ago
Identify the graphed linear equation.
Veseljchak [2.6K]

Answer:

Where is the graph.

Step-by-step explanation:

Where is the graph.

7 0
3 years ago
Read 2 more answers
What is 3.754×10^5 than round it to the tenth
saul85 [17]

Answer:

375,400

Step-by-step explanation:

  1. 3.754*10^5
  2. 10^5=100,000
  3. 3.754*100,000
  4. 375,400

YaYYYY u got it! =)

5 0
3 years ago
Read 2 more answers
The computed chi-square value is positive because the difference between the observed and expected frequencies is
Pani-rosa [81]
The frequencies is small
5 0
3 years ago
11. Twenty-four students in Jamal's class are wearing tennis shoes. There are
RUDIKE [14]

Answer: Incorrect.

Step-by-step explanation: 24 out of 30 is 80.00%.

Step 1: We make the assumption that 30 is 100 % since it is our output value.

Step 2: We next represent the value we seek with x.

Step 3: From step 1, it follows that 100 % = 30.

Step 4: In the same vein, x % = 24 .

Step 5: This gives us a pair of simple equations:

100 % = 30(1).

x % = 24(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

100 % / x % = 30/24

Step 7: Taking the inverse (or reciprocal) of both sides yields

x/100 = 24/30

x = 80 %

3 0
1 year ago
Read 2 more answers
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