The roots of an equation are simply the x-intercepts of the equation.
See below for the proof that [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex] has at least two real roots
The equation is given as: [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex]
There are several ways to show that an equation has real roots, one of these ways is by using graphs.
See attachment for the graph of [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex]
Next, we count the x-intercepts of the graph (i.e. the points where the equation crosses the x-axis)
From the attached graph, we can see that [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex] crosses the x-axis at approximately -2000 and 2000 between the domain -2500 and 2500
This means that [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex] has at least two real roots
Read more about roots of an equation at:
https://brainly.com/question/12912962
