Find ALL real roots! – Polynomial function

In this math video I (Susanne) explain how to find the real roots of the function with x to the power of 3. We factorise the polynomial and solve for x.

00:00 Intro – Roots of a function
0:07 Example 1
3:30 Example 2
5:47 See you later!

*My German Math Channel:*
@MathemaTrick

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#maths #learning #roots

[mattjordan]

Susanne, you are the greatest thing that has happened to math since Isaac Newton! Your spirit is awesome and makes learning math fun! Keep making the fun and informative content!

[davepowder]

I notice that the subscriber count for our Math Queen is going up and up and up. Lots of older and newer math-brains coming to refresh and grow their minds! 😎

[ZGT]

Thank you for your instruction. I really enjoy your instruction.

[com]

Ah, no ridiculous English AI "translation" - just a real Susanne! Vielen Dank!

[feerrnn]

Hello, Susanne.
I’m not sure if you remember me, but I used to follow you and Thomas for Moonsun content.
I recently found your new channel, and I’m so glad to see you're back! It's now focused on math instead of music, but you're still doing an incredible job, so I’ll definitely stick around.

[brianwade]

At 3:04 and 5:25, you should get into the habit of writing the RHS square root with a +- prefix.

[brucea]

In your response to my comment about the distinction between "root" and "zero" you said you are not a native speaker. But you sound like a native English speaker to me. I am wondering what is your native language.

[JessWLStuart]

I love your videos Susanna! What presentation software are you using?

[ScottTaylorMCPD]

Great video, but you should include an addendum on finding the imaginary roots for the second example.

[יהודהבלאס]

It’s been a long time since I last studied mathematics, and I’m really enjoying the journey and the way you explain the exercises—it's simply fun!! Thank you!

[jeffbuxton]

Math Queen- Can you solve this? A rectangle has a diagonal that measures 5. A perpendicular off of it to a corner measures 2. Find the area and all other sides including the sections of the diagonal on either side of the perpendicular

[mbhla]

You and your channel are just FANTASTISCH!!!!

[abhijeetm]

Ich glaube, dass du doch ein Deutsches Kanal hast, oder?
Ich hab ihn abonniert, um meine Deutsch zu verbessern.
Viele Grüße 🎉😊

[megakrypt]

At, 0 = x^3 - 4 x, I would have divided both sides by x giving 0 = x^2 - 4 then added 4 to both sides giving 4 = x^2. Sorry. Couldn’t type plus/minus symbol. Is your working more reliable for harder examples or anything or this this just there are different ways to get to the answer?

[Satishstar]

Find real root x power 5+ 2 x square+3

[mjeghss]

Could you show me how do you make video??
Maybe I want to make video in my language. PLz ❤❤❤❤❤

[davepowder]

Mz. Susanna, I just noticed that your German math channel link gives me a not-found error?

[paulsmith]

What is the difference between complex numbers and imaginary numbers?

[coel]

I would of taken the time to do a difference of squares. You would have 3 equations equals zero.


Second problem, remove 2x instead.

[m.h.]

Solutions:



If you have a polynomial without a constant, x = 0 is always a root!
Therefore you can just extract one x and calculate the roots for the rest.
(1)
x² - 4 = 0
x² - 2² = 0
(x + 2)(x - 2) = 0
x ∈ {-2, 0, 2}

(2)
2x² + 8 = 0 |:2
x² + 4 = 0 |-4
x² = -4
no other real solutions!
x = 0