Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.