Question

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

Answer 1

Simplifying 4x4 = 12x2 Solving 4x4 = 12x2 Solving for variable 'x'. Reorder the terms: -12x2 + 4x4 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -12x2 + 4x4 = 0 Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(-3 + x2) = 0

Answer 2

we have

`4x^5-12x^4+6x=5x^3-2x`

Separate the equation above in two equations

equation
`1`

`y=4x^5-12x^4+6x`

equation
`2`

`y=5x^3-2x`

we know that

In a system of equations the roots of the equation
`1` must satisfy equation
`2` and the roots of the equation
`2` must satisfy equation
`1`

therefore

the answer is

The system of equations is

`y=4x^5-12x^4+6x`

`y=5x^3-2x`