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

Sagot :

MrRoyal

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

View image MrRoyal
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