If fxx4 1 calculate x1x2x3x4 and x12x22x32x42SolutionUsing

If f(x)=x^4 + 1 calculate x1+x2+x3+x4 and x1^2+x2^2+x3^2+x4^2.

Solution

Using the Viete expressions, which are the connection between roots and coefficients of an equation:

x1 + x2 + x3 + x4=0

x^2 + x2^2 + x3^2 + x4^2 = (x1 + x2 + x3 + x4)^2 - 2(x1*x2 + x1*x3 + x1*x4 + x2*x3 + x2*x4 + x3*x4)

x1*x2 + x1*x3 + x1*x4 + x2*x3 + x2*x4 + x3*x4= c/a=0/1=0

x^2 + x2^2 + x3^2 + x4^2 = 0 - 2*0=0