How to find number of turning points of polynomial using Formula from equations with 5 examples

CAUTION: The formula discussed for the number of turning points will not work when we have imaginary roots. It always works for Real roots. Thanks

[farzonaizatullaeva]

I was struggling with these types of questions, but after your explanation, I started getting every question correct! Thank you.

[alanlei]

This guy's voice is oddly satisfying. Nice vid tho.

[abeshekkalimuthu]

WOW.. What a great video, your method is very easy to understand! Thank you!

[ericbian]

it doesn't work for (x^2+1)(x-3)(x+4), it actually has 3 turning points, but the formula shows 1 turning point

[chulachose]

Thanks so much for making this video helped me a lot!

[sameerchaudharivlogs]

Hi Sir, is there a book/pdf which explains the proof of this formula ?

[haseebchowdhury]

Thanks for helping me with my tomorrow's quiz

[keig_mstpdg]

Woah! This is so so helpful. Thanks so much!!

[shiro]

thank you so much, made it way easier

[prrnce]

Is it possible to get a 0 turning point?

[tomscott]

nice work. it helps a student i'm tutoring

[ericbian]

And also I was struggling with a question: what will happen to the graph if you add 2 imaginary roots? for example (x^2+1)(x-3)(x+4) has three turning points but (x^2+1)(x-1)(x+1) only has one turning point. I can tell that the graph stretches, but does it also add turning points?

[ericbian]

It also wouldn't work for even degree polynomials that don't have any real zeros

[murvs]

Great video. Idk if you've fixed this but there's an excessive amount of lip smacking, might want to work on that. :)

[dhyeysuvagiya]

Ye to tatti hai 🤨 simple- highest degree -1 should be the formula