# Math Help - Sketch graph help

1. ## 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.

2. 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 $x^4 = 1 - 3x$

or $x^4 + 3x - 1 = 0$.

So what does the number of times the two graphs cross tell you about the number of roots of $x^4 + 3x - 1 = 0$?

3. 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.