what does ordered pair means?

Question

If the eqn x^4-4x^3+ax^2+bx+1=0 has four positive roots , the ordered pair (a,b) is

(1)(-4,6)

(2)(6,-4)

(3)(-2,-3)

(4)(-3,2)


what does ordered pair means here ?
i dont understand this term in this context.

the equn has 4 roots that i believe ..........what does ordered pair means here ?

somebody ,plz explain this question

Answer 1

For the equation of the 4th degree polynomial

x^4 - 4x³ + ax² + bx + 1 = 0

Find a and b such that the polynomial has four positive roots. The ordered pair (a, b) are the coefficients of the x squared and x terms.

The answer is

(2) (a, b) = (6, -4)

x^4 - 4x³ + ax² + bx + 1 = 0
x^4 - 4x³ + 6x² - 4x + 1 = 0
(x - 1)^4 = 0
x = 1

All four roots are 1 and therefore positive. It is a quadruple root.

Answer 2

Ordered Pair is a collection of x - coordinated and y - coordinated. The horixontal axis is called the x -axis and th vertical axis is called the y - axis. the ordered pair of (- 4, 6). The - 4 is called the x - coordinated and the 6 is called the y- coordinates.

To Locate tne coordinates on a graph

(- 4, 6)

Move left horizontal from the origin - 4 places and vertically up 6 places.

(6, 4)

Move right horizontal from the origin 6 places and vertically up 4 places.

(- 2, - 3)

Move left horizontal from the origin- 2 places and vertically down - 3 places.

(- 3, 2)

Move left horizontal from the origin - 3 places and vertically up 2 places.

- - - - - - -

Roots

(- 4, 6)

x = - 4

Transpose 4

x + 4 = - 4 + 4

x + 4 = 0

The - 4 is the root

- - -

y = 6

Trnspose 6

y - 6 = 6 - 6

y - 6 = 0

the 6 is the root

- - - - - - - -s-

Answer 3

An ordered pair is simply the x and y coordinates of the equation or (a,b) in this case.

So, if you were to substitute one of those four ordered pairs, one will give you four positive roots.

Answer 4

ordered pair means the value of a and b. it's just like algebra where in the ordered pairs are represented as (x,y) which stands for the value of x and y.

Answer 5

Let (a, b) and (x,y) be two order pairs such that (a,b)=(x,y)

Then a=x and b=y.

In Set Theory (a,b) = {a,{a,b}}