which system of equations can be used to find the roots of the equation $4x^{2}=x^{3}+2x$?\n$\begin{cases}y…

which system of equations can be used to find the roots of the equation $4x^{2}=x^{3}+2x$?\n$\begin{cases}y = - 4x^{2}\\y=x^{3}+2xend{cases}$\n$\begin{cases}y=x^{3}-4x^{2}+2x\\y = 0end{cases}$\n$\begin{cases}y = 4x^{2}\\y=-x^{3}-2xend{cases}$\n$\begin{cases}y = 4x^{2}\\y=x^{3}+2xend{cases}$

which system of equations can be used to find the roots of the equation $4x^{2}=x^{3}+2x$?\n$\begin{cases}y = - 4x^{2}\\y=x^{3}+2xend{cases}$\n$\begin{cases}y=x^{3}-4x^{2}+2x\\y = 0end{cases}$\n$\begin{cases}y = 4x^{2}\\y=-x^{3}-2xend{cases}$\n$\begin{cases}y = 4x^{2}\\y=x^{3}+2xend{cases}$

Answer

Explanation:

Step1: Recall root - finding concept

The roots of an equation (f(x)=g(x)) are the (x) - values where the graphs of (y = f(x)) and (y = g(x)) intersect.

Step2: Analyze the given equation

The given equation is (4x^{2}=x^{3}+2x). To find its roots using a system of equations, we can set (y = 4x^{2}) and (y=x^{3}+2x). The solutions of the system (\begin{cases}y = 4x^{2}\y=x^{3}+2x\end{cases}) will be the (x) - values for which (4x^{2}=x^{3}+2x), which are the roots of the original equation.

Answer:

(\begin{cases}y = 4x^{2}\y=x^{3}+2x\end{cases})