integer help?

Question

Use graph of f(x) = 3x^4 + -7x^2-2x-3 to find the smallest postitive integer that is an upper bound and the largest negative integer that is a lower bound for hte real roots for 3x^4 + -7x^2-2x-3=0
Then use synthetic division to show that all the real roots of the equation lie between these integers.

Please help me.....

Answer 1

Well, I can't show the graph here, but I graphed
it on my graphing calculator and all the
real roots lie between -2 and 2.
You can make a graph of this online at coolmath.com
Let's look at f(-2): It equals 48-28 + 4-3>0
f(-1) = 3-7+2-3<0.
So there is a real root between -2 and -1.
(You can calculate f(-2) and f(-1) by synthetic division.)
Similarly, there is a real root between 1 and 2.
The graph shows there are only 2 real roots.
We can use Rolle's theorem to confirm this.