Question

Which system of equations can be used to find the roots of the equation 4x2 =x3 +2x?

Answer 1

The system of equations are $\boxed{y = 4{x^2}}{\text{ and }}\boxed{y = {x^3} + 2x}$ that can be used to find the roots of the equation $4{x^2} = {x^3} + 2x.$

Further explanation:

Given:

The equation is $4{x^2} = {x^3} + 2x.$

Explanation:

The given equation is $4{x^2} = {x^3} + 2x.$

Consider the left hand side of the equation $4{x^2} = {x^3} + 2x$.as y and the right hand side of the equation $4{x^2} = {x^3} + 2x$ as y.

$\begin{aligned}y&= 4{x^2} \hfill\\y&= {x^3} + 2x \hfill\\\end{aligned}$

To obtain the roots of the system of equation we have to solve the equations.

The system of equations are $\boxed{y = 4{x^2}}{\text{ and }}\boxed{y = {x^3} + 2x}$ that can be used to find the roots of the equation $4{x^2} = {x^3} + 2x.$

Learn more:

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Polynomials

Keywords: polynomial, solution, linear equation, quadratic equation, system of equations, solution of the equations, $4x2 = x3 + 2x$, roots, roots of equation.

Answer 2

Answer:

$\left \{ {{y=4x^2} \atop \\ \\ {y=x^3+2x}} \right.$

Explanation:

An equality can be transformed in a system of equations by making each side equal to a new variable. In this case the variable y was made equal to each side.

See that may find the solution of such system by graphing both functions in a same coordinate system, where the intersection of the functions would show the solution of the system.

I show you that in the attached image. In such graph, the red curve is the function y = x² and the blue function is y = x³ + 2x.

The intersection point is (0,0) meaning that the solution is x = 0, y = 0.