Question

Which system of equations can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x?

A). Y=-4x^5+12x^4-6x and y=5x^3-2x
B). Y=4x^5-12x^4+5x^3+4x and y=0
C). Y=4x^5-12x^4+6x and y= -5x^3+2x
D). Y=4x^5-12x^4+6x and y=5x^3-2x

Answer 1

D is the answer......................

Answer 2

D). Y'=
`4x^(5)-12x^(4)+6x` and y'=
`5x^(3)-2x`

Explanation:

We are given the equation
`4x^(5)-12x^(4)+6x=5x^(3)-2x`.

On simplifying this equation, we get
`4x^(5)-12x^(4)-5x^(3)+8x=0`

i.e. Let, Y'=
`4x^(5)-12x^(4)+6x` and y'=
`5x^(3)-2x`

Now, according to the options,

A) Y =
`-4x^(5)+12x^(4)-6x` = -Y' , that means the graph will be inverse of the required graph.

B) As the coefficient of 'x' in our given equation and the equation of option B are different, both will have different graphs.

C) As y =
`-5x^(3)+2x` = -y', this means that the graph will be inverse of the required graph.

Hence, all above options are discarded and so option D is correct.