Cubic Roots

Algebra Level 4

Let \(x=a\), \(y=b\) and \(z=c\) be the solutions of the simultaneous equations \[\begin{align} x+y+z &= -71, \\ 4x+2y+z &= -32, \\ 9x+3y+z &= -27. \end{align} \] Then the three roots of the cubic equation \(t^3+at^2+bt+c=0\) are \(\alpha\), \(\beta\) and \(\gamma\), where \(\alpha< \beta< \gamma\). What is the value of \(100\alpha+10\beta+\gamma\)?

×

Problem Loading...

Note Loading...

Set Loading...