The sum of the roots of this polynomial

Question

The polynomial is x^3-x^2-18x+k

Answer 1

Let the roots be a, b, c.

Then

x³ - x² - 18x + k = (x-a)(x-b)(x-c) =

x³ - ax² - bx² - cx² + abx + acx + bcx - abc =

x³ - (a+b+c)x² + (ab+ac+bc)x - abc

When two polynomials are equal for all x, then their respective coefficients

are equal. Therefore

a+b+c = 1