Question

Show that the equation x^4/2021 − 2021x^2 − x − 3 = 0 has at least two real roots.

Answer 1

The roots of an equation are simply the x-intercepts of the equation.

See below for the proof that $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$ has at least two real roots

The equation is given as: $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$

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 $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$

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 $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$ crosses the x-axis at approximately -2000 and 2000 between the domain -2500 and 2500

This means that $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$ has at least two real roots

Read more about roots of an equation at:

brainly.com/question/12912962