Dear Colleagues, see this video on the diagonalisation of a 3x3 matrix.
My question exactly is about the method used at the minute 5:00 to 5:21 to find the roots of the polynomial.
This is the link of the video:
https://youtu.be/Sf91gDhVZWU
Thank you dear George for the link. Yes, If a is a root then, just the division of the polynomial by X-a. The best in this link is the table which contains the coefficients, it makes it very easy to find the result of the division. But my question is how the teacher found directly and easily the root a=-2
I think there is no special method to find the root a, but we know that the constant coefficient is equal to the product of all the roots. So we just look for its divisors and try one by one, and this what did the teacher without mentioning that. What do you say dear George?
It called Horner's method for polynomial factorization. You can consult E.B Vinberg graduate text on Algebra.
He used Horner's methods at the end but he started by trying -2 as a root for the charactestic polynomial sice it is known that a rational root for a monic polynomial shoud be a divisor for the constant term which is -16 in this case so he had to try one of the divisors of -16 so he started with -2 which turns out to be a root then he divided the polynomial by X+2 ...etc
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics