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

Question

asked Jun 19, 2020 157k views

2 Answers

Jayshao · Answer 1 · 2020-06-25T20:51:10+0000

Answer:

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
$x^(3)+2 x^(2)-11 x-12 \text { is }-2$