Theory of Equations

[vijay1965]

1) if alpha, beta and gamma and delta are the roots of the equation x4+px3+qx2+rx+s=0.find the values of ∑ ( alpha/beta)
2) if alpha, beta and gamma and delta are the roots of the equation x4+px3+qx2+rx+s=0.find the values of ∑ (1/alpha)
3) if alpha, beta and gamma and delta are the roots of the equation x4+px3+qx2+rx+s=0.find the values of ∑ (alpha/beta + beta/alpha)

 

[HallsofIvy]

1) if alpha, beta and gamma and delta are the roots of the equation x4+px3+qx2+rx+s=0.find the values of ∑ ( alpha/beta)
2) if alpha, beta and gamma and delta are the roots of the equation x4+px3+qx2+rx+s=0.find the values of ∑ (1/alpha)
3) if alpha, beta and gamma and delta are the roots of the equation x4+px3+qx2+rx+s=0.find the values of ∑ (alpha/beta + beta/alpha)

You have [math](x- \alpha)(x- \beta)(x- \gamma)(x- \delta)= x^4+ px^3+ qx^3+ rx+ s= 0[/math].
Multiply the left side and compare coefficients.