Question

what is the sum of the roots of the polynomial shown below? f(x)=3x^3+12x^2+3x-18

Answer 1

well given the polynomial

\[P(x) =ax^3 + bx^2 + cx + d\]

and if it has roots

\[\alpha, \beta, \gamma \]

then the sum of the roots is

\[\alpha + \beta+ \gamma = \frac{-b}{a}\]

in your question a = 3 and b = 12

hope it helps

Answer 2

\[f(x)=3\left( x^3+4x^2+x-6 \right)\]

f(1)=0

Answer 3

\[f(x)=\left( x-1 \right)\left( x^2+5x+6 \right)\\ f(x)=(x-1)(x+2)(x+3)\]

1-2-3 = -4 .. same as campbell_st ... answer verified