Question

Which system of equations can be used to find the roots of the equation 4x²=x²+2x?

a) 2y=−4x²
b) y=x²+2x
c) y=x²−4x²+2x
d) 0x=0

Answer 1

The system of equations to find the roots of the equation 4x²=x²+2x is given by y=4x², and y=x²-4x²+2x, which corresponds with answer choice (c).

Step-by-step explanation:

The student is asking which system of equations corresponds to finding the roots of the quadratic equation 4x²=x²+2x. First, we need to get this equation in the standard quadratic form ax²+bx+c = 0. Subtracting x² and 2x from both sides yields 3x²-2x = 0, which is the standard form.

In order to create a system of equations, we need two separate equations. The original equation 4x²=x²+2x can be considered as one equation, which can be rearranged to y=4x² for comparison with the answer choices. Considering the standard form 3x²-2x = 0, we can assign y=x²-4x²+2x to set up the second equation by equating y with the left-hand side of the equation, taking into account the transposition of terms.

This leads to the system of equations corresponding to answer choice (c):

1. y=4x²
2. y=x²-4x²+2x