which system of equations can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x?
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
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
\(y=4x^5-12x^4+6x\)
\(y=5x^3-2x\)