Question

how to find the roots of the equation X^3- 10x^2+ 7 x + 18 = 0
alpha beta gamma?

Answer 1

Looking at the coefficients we can quickly say that: -1 is a root.

Express the given expression on the LHS as a product of two factors:
(x+1)(a x^2 + b x + c)
Looking at the coefficients and comparing with the given polynomial, we can decide a=1 and c= 18.

Expand the product and find b.

Now factorize the quadratic polynomial and find the Roots. b will be - 11. Alpha is -1. Others will be 2 and 9.