Question

What is the sum of the roots of the polynomial shown below?
f(x) = x^3 + 2x^2 - 11x-12

Answer 1

Answer: -2

Explanation:

(A.pex)

Answer 2

Sum of the roots of the polynomial
`x^(3)+2 x^(2)-11 x-12 \text { is }-2`

Solution:

The general form of cubic polynomial is
`a x^(3)+b x^(2)+c x+d=0` ---- (1)

If we have any cubic polynomial
`a x^(3)+b x^(2)+c x+d=0` having roots
`\alpha , \beta , \theta`

Sum of roots
`\alpha + \beta + \theta` =
`(-b)/(a)` ---(2)

From question given that,

`x^(3)+2 x^(2)-11 x-12` --- (3)

On comparing equation (1) and (3), we get a = 1, b = 2, c = -11 and d = -12

Hence the sum of roots using eqn 2 is given as,

=
`(-2)/(1)`

= -2

Hence the sum of the roots of the polynomial
`x^(3)+2 x^(2)-11 x-12 \text { is }-2`