what is the sum of the roots of the polynomial shown below

Question

f(x)=3x^3+12x^2+3x-18

Answer 1

Given that

Substitute the value of x=1

f(1) = 0

That means  (x-1) is a factor for the given equation

Take 3 common

3 is also a factor

Take (x+3) common

The remaining factors are (x+2) (x+3)

The  factors the given polynomial is (x-1) (x+2) (x+3)

Therefore the  roots of the given polynomial is (x-1) = 0 ==> x = 1

                                                                       (x+2) =0 ==> x = -2

                                                                       (x+3) = 0 ==> x = -3

The sum of the roots are 1 - 2 - 3 = -4

 

Answer 2

The polynomial is f (x) = 3x³ + 12x² + 3x - 18.

Sum of the roots of the third degree polynomial = - x² coefficient / x³ coefficient.

Here, x² coefficient = 12 and x³ coefficient is 3.

Therefore, sum of the roots of the given polynomial = - 12/3 = - 4.