how do u find possible number of real roots?

Question

for an equation like 2x^5-4x^4-4x^2+5=0??????
or any equation?
like how can u find wat they r and how many their r?

Answer 1

Well, the maximum possible number is the degree of the polynomial. I.e., the largest exponent, namely 5.

And the minimum number of roots of a polynomial with odd degree is 1, because it goes to plus infinity in one direction and minus infinity in the other direction, and being continuous must cross all finite values inbetween.

As for finding them. You surely know the quadratic formula, and there are similar formulas for 3rd and 4th degree polynomials. After that, however, it becomes a lot more problematic, if you can't happen to find a rational root or some other root by trial and error.

The one you wrote, by the way, has no rational roots.