Thread: Sketch graph help

The question states:

Sketch the graphs of y = x^4 & y = 1-3x. Deduce the number of real roots of the equation: x^4+3x-1

I have sketched both graphics, but I am un-sure as how to prove that the graph has n number of real roots.

Thank you.

Originally Posted by StephenPoco

The question states:

Sketch the graphs of y = x^4 & y = 1-3x. Deduce the number of real roots of the equation: x^4+3x-1

I have sketched both graphics, but I am un-sure as how to prove that the graph has n number of real roots.

Thank you.

The graphs cross where the equations are equal:

So

or .


So what does the number of times the two graphs cross tell you about the number of roots of ?

Oh, I see. So when the two graphs "combine" per se, their intersections become the roots? Well in that case there are 2 roots.

Thanks.