What does the Rational Root Theorem and Descartes' Rule of Signs indicate about the zeros of a polynomial function?

Answers

Answer 1

Answer:

Answer:

"Descartes' rule of sign is used to determine the number of real zeros of a polynomial function. It tells us that the number of positive real zeroes in a polynomial function f(x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients."

Explanation:

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Answer 2

Answer:

Final answer:

The Rational Root Theorem provides possible rational roots of a polynomial while Descartes' Rule of Signs indicates the number of positive and negative roots of a polynomial. They both serve as crucial tools in understanding and solving polynomial equations.

Explanation:

The Rational Root Theorem and Descartes' Rule of Signs are both mathematical tools that can provide valuable information about the zeros (or roots) of a polynomial. The Rational Root Theorem can help us determine the possible rational roots of a polynomial equation. It states that if a polynomial has a rational root p/q (where p and q are relatively prime), then p is a factor of the trailing constant and q is a factor of the leading coefficient.

On the other hand, Descartes' Rule of Signs gives us an indication of the number of positive and negative real roots in a polynomial. It does this by considering the number of sign changes in the coefficients of the terms of the polynomial when arranged in descending power.

For example, in the polynomial $x^3 - 3x^2$ + 2x - 6, by applying Descartes' Rule of Signs, we can infer there are two or zero positive roots (since there are two sign changes) and one negative root (since there are no sign changes when the terms are arranged in ascending power).

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Two times Noura's age plus 5 years equals Ali's age. Ali is 19 years old. What formula could be used to calculate Noura's age

Answers

Answer:

Noura is seven years old

Step-by-step explanation:

to get Noura's age first you need to subtract 5 years from Ali's age which will get you to 14 years of age now you just need to divide 14 by two to get Noura's age which is seven

What is the value of 2.57 1.75

Answers

Answer:

2.57 - 1.75 = 0.82

Step-by-step explanation:

Let us assume that we need to find the value of 2.57 - 1.75 i.e. we need to subtract 1.75 from 2.57. It can be done as follows :

The first number is 2.57 and other no is 1.75.

In 2.57, 2 is in ones place, 5 is in tenths place and 7 is in hundredths place.

In 1.75, 1 is in ones place, 7 is in tenths place and 5 is in hundredths place.

Subraction :

2.57

- 1.75

= 0.82

Hence, the value of 2.57 - 1.75 is 0.82

which polynomials are in standard form? A. t^4-1 B. -2t^2+3t+4 C. 4t-7 D. None of The Above Choose all answers that apply

Answers

Answer:

B. -2t^2+3t+4

Step-by-step explanation:

The standard form as

ax^2 + bx + c

Option B meets that requirement, even though it has a '-' in front

Final answer:

All the given polynomials, A. t^4-1, B. -2t^2+3t+4 and C. 4t-7 are in standard form since their terms are written in descending order of their degrees.

Explanation:

In mathematical terms, a polynomial is in standard form if its terms are written in descending order of their degree, i.e. the power of the variable. This means the term with the highest power should be listed first, followed by the term with the next highest power, and so on. Let's look at the options:

Option A: t^4-1 is in standard form because t^4 is the highest degree term and it is listed first.
Option B: -2t^2+3t+4 is also in standard form as the terms are arranged in descending order of degree: 2 (in t^2), 1 (in t) and then 0 (in 4).
Option C: 4t-7 is in standard form as well, with the degree of the term 4t being 1 and the degree of -7 being 0.

So, in conclusion, the polynomials in standard form from the provided options are A. t^4-1, B. -2t^2+3t+4 and C. 4t-7.

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Which of the following functions has a range of all real numbers?

Answers

Answer:

Step-by-step explanation:

The dots cannot intersect

Final answer:

A function having a range of all real numbers is a function where any output value can be achieved. An example is y=sinx, which oscillates continuously between -1 and 1, thus covering all real numbers in its range.

Explanation:

The function which has a range of all real numbers is a function where any output (y-value) is possible, irrespective of the input. The range of a function is the complete set of possible output values (y-coordinates), which result from using the function formula. An example of a function with a range of all real numbers is y=sinx. Since y=sinx oscillates between -1 and 1, given a large number of repetitions (or a continuous plot from -infinity to +infinity), all real numbers in your range (-1 to 1) are represented.