Without solving the corresponding equation, find the sum of the three roots of the polynomial
$$2x^3 − 8x^2 + 20x − 19$$
I know that sum of the roots is $-b/a$ which is $-(-8)/2 = 4$ however I'm not confident in my answer because it seems to simple, could anyone please help explain.
note: still new to this not too sure how to format polynomials correctly if anyone could help with that as well
Best Answer
Let $a,b,c$ the complex roots. Then the factorization of $p$ is
$p=2(x-a)(x-b)(x-c)=2x^3-2(a+b+c)x^2+2(ab+bc+ac)x-2abc$.