Question

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

Answer 1

Answer:

The system of equations form is $y=4x^2$ and $y=x^3+2x$  and roots of the roots of the equation are x=0 and x=0.5861.

Step-by-step explanation:

Given : Equation $4x^2=x^3+2x$

To find : Which system of equations can be used to find the roots of the equation?

Solution :

To form the system of equation an equality is formed by making each side equal to a new variable.

So, The system of equations form is

$y=4x^2$ .....(1)

$y=x^3+2x$  .....(2)

Now, To solve the system of equation we solve it graphically,

Plot both the equations,

$y=4x^2$ represented with green line.

$y=x^3+2x$ represented with red line.

Refer the attached figure below.

Now, the intersection of both the lines are the solution of the system.

The intersection points are (0,0) and (0.586,1.373).

The roots of the equation are x=0 and x=0.5861.

Therefore, The required answers are

The system of equations form is $y=4x^2$ and $y=x^3+2x$  and roots of the roots of the equation are x=0 and x=0.5861.

Answer 2

Next time, please share the answer choices.
Starting from scratch, it's possible to find the roots:

4x^2=x^3+2x should be rearranged in descending order by powers of x:

x^3 - 4x^2 + 2x = 0.  Factoring out x:  x(x^2 - 4x + 2) = 0

Clearly, one root is 0.  We must now find the roots of (x^2 - 4x + 2):

Here we could learn a lot by graphing.  The graph of y = x^2 - 4x + 2 never touches the x-axis, which tells us that (x^2 - 4x + 2) = 0 has no real roots other than x=0.  You could also apply the quadratic formula here; if you do, you'll find that the discriminant is negative, meaning that you have two complex, unequal roots.