Question

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

Answer 1

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 $\alpha + \beta + \theta$ = $\frac{-b}{a}$ ---(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,

= $\frac{-2}{1}$

= -2

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