wishmaster said:I know how to find the roots with Horners method
mathbalarka said:You don't have to go that far. Try proving that this factors over integers completely by applying rational root theorem (integral root theorem for monic polynomials).
wishmaster said:I have given polynomial: \(\displaystyle x^3-8x^2+19x-12\)
I know how to find the roots with Horners method,i am just wondering if there is an easier and quicker way to find them? Thank you!
wishmaster said:I don't know how to do it...
mathbalarka said:
wishmaster said:Seems that's not the easier and faster method as Horners...or i can't see it! :D
chisigma said:... not only neither easier nor faster... if the polynomial doesn't have rational roots [... the most probable case...] it fails!(Tmi)...
Kind regards
$\chi$ $\sigma$
chisigma said:neither easier nor faster
mathbalarka said:Horner's method has computational complexity $\mathcal{O}(n)$, whereas RRT exceeds that quite less often, as far as I can tell.
The roots of a polynomial are the values of the variable that make the polynomial equal to zero.
To find the roots of a polynomial, you can use various methods such as factoring, the quadratic formula, or synthetic division.
The roots of a polynomial are the solutions to the polynomial equation, while the factors of a polynomial are the expressions that multiply together to make the polynomial. The roots and factors of a polynomial are related because the roots of a polynomial correspond to the factors of the polynomial equation.
Yes, a polynomial can have multiple sets of roots depending on its degree. For example, a quadratic polynomial can have two distinct sets of roots, while a cubic polynomial can have three sets of roots.
The roots of a polynomial are important because they provide valuable information about the behavior and characteristics of the polynomial. They can help determine the x-intercepts, the turning points, and the overall shape of the polynomial's graph.