IIT Kanpur Sample

Question

3. Let α, β, γ be roots of equation x^3 + 3x^2 + 2x + 12. Then α^2 + β^2 + γ^2 is equal to .

Answer 1

using $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab+bc+ca)$;

            $a^{2} + b^{2} + c^{2} = (a + b + c)^{2} -  2(ab+bc+ca) $

For Equation of the form, $\alpha x^{3} + \beta x^{2} + \gamma x + \delta$,

$a+b+c = -\frac{\beta }{\alpha }$    

and $ab+bc+ac = \frac{\gamma }{\alpha }$    

So clearly its equal to 9-2*2 = 5;

Ans  =  5