'Rooty' polynomial!

Given polynomial : $x^3 - 27x^2 - 3081x - 3053 = 0$

By possible rational root theorem , we can easily figure out that $-1$ is a root of this polynomial.

Thus, By Factor theorem , $(x + 1)$ is a factor of $x^3 - 27x^2 - 3081x - 3053 = 0$ .

Thus by Division algorithm the given polynomial can be written as :

$x^3 - 27x^2 - 3081x - 3053 = (x + 1)(x^2 - 28x - 3053) = 0$

Since we have already got $-1$ as a root ,

$(x^2 - 28x - 3053) = 0$

$(x - 71)(x + 43) = 0$ This gives us that $71 , -43$ are the other roots of the polynomial.

Thus , $a = 71 , b = -1 , c = -43 \Rightarrow 2a + 7b + c = 2(71) + 7(-1) + (-43) =\huge\boxed{92}$

Very easy solution is that Take your casio calculator .press MODE and select eq.then tell all co-efficient and in the last press equal(=) . You ll get these 3 Ans.. but that will be a big loss for you that you cant approaches to ans without calculator... I done it by both to verify myself either Am I right Or Am I right??