Hey ryu1.
Hint: Consider the second derivative being 0 and how that correlates with the information about the roots.
Also do the roots have to be real or can they be complex as well?
Hi,
I am asked to prove a 4th degree polynomial:
p(x) = x^4+x^3-3
Has at least 2 roots...
And that some other equation doesn't roots in interval (-oo,-2)
and that it has 3 roots in (-oo,+oo)
what does it means that an equation has roots? or to find it?
like with the quadratic formula that you find the +- x's ? (is has either 1 or 2 right?)
Is there a simple way to find roots of such equations (with x^3 or higher degree)?
Thanks (again).
A root of a polynomial is a number such that . For example the roots of a quadratic equation is given by the quadratic formula. For a more concrete example, the number is a root for the polynomial since .what does it means that an equation has roots? or to find it?
Not in general. There are some truly monstrous equations for general polynomials of degree 3 and 4. However, it has been proven that such an formula is impossible for degrees 5 and higher (not just unknown, but cannot possibly exist). So your best bet in these questions is to look for properties for your specific polynomial, not a general one. I cannot guarantee I can give you an answer which you can understand without knowing how much you know, but here is an attempt.Is there a simple way to find roots of such equations (with x^3 or higher degree)?
This approach is different from chiro's, so you can choose what you like. First, we note that as , so there is some number such that and . Next, we see that is negative at some point, for example . Applying the intermediate value theorem on and gives the result.I am asked to prove a 4th degree polynomial:
p(x) = x^4+x^3-3
Has at least 2 roots...