Question

Hello,
How do I use the intermediate value theorem to prove a function has THREE roots. I know how to prove one real root!

Answer 1

please help

Answer 2

are you trying to do a rigorous proof or can we plug and chug till we get the result? is this for an algebra class?

Answer 3

no its for a calculus exam. i will post the question

Answer 4

Use the Intermediate Value Theorem to show that
3x^2 = x^3 + 3
holds for three real values in the range -1<= x <=3.

Answer 5

well if the graph is continuous it will have an infinite amount of real values between -1 and 3. is there a more complex explanation needeD?

Answer 6

I understand that but is there away of proving there is 3 roots between the 2 intervals?

Answer 7

well if you get all your values one one side of the equal sign we know that it is a cubic function and we know cubic functions are continuous curves. with endpoints going in opposite directions. so we know that between -1 and 3 there exists 0,1,2. to make the numbers stick out. unless you want a rigorous proof. i think there is a way to plug your interval in to find this out. but you will have to give me a sec. this was all a while back.

Answer 8

Ok thats not to complicated so... Thanks for the help by the way

Answer 9

have you tried plugging each number i just gave you between the interval into the function? there should be many sign changes

Answer 10

i just did it there and i made a graph... i then plotted the points and sort of connected them... it has 3 real roots! THANK YOU very much i completely understand now

Answer 11

sweet. i was afraid i didn't do you any good at first

Answer 12

freakout is now over... i can relax!