153 views
0 votes
0 votes
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 .

1 Answer

2 votes
2 votes
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

Related questions

0 votes
0 votes
1 answer
1
Shubham Pandey 2 asked Apr 13, 2018
184 views
4 What is the unit eigenvector corresponding to minimum eigenvalue of matrix1 -1-1 1
2 votes
2 votes
1 answer
2
Saisha Narang 1 asked Apr 29, 2018
447 views
A symmetric matrix X is said to be diagonalizable if we can express it as X = P DP −1 where P is an invertible matrix and D is a diagonal matrix. For a diagonalizable m...