If we have the expression E = x^4 + 4 calculate x1 + x2 +x3 + x4 where x1,2,3,4 roots of the equation E.
This is a 4 degree function, then it has 4 roots (x1,x2,x3,and x4)
The standard formula for the function is:
According Viete's rule, we know that:
E(x) = x^4+4.To find the root the sum x1+x2+x3+x4 where x1,x2,x3 and x4 are the solutions of x^4+4 = 0.
x^4+4 = 0 is a polynomial equation of the form:
x^4+0*x^3+0*x^2+0/*x+4 = 0.
So the sum of the roots = - coeeficient of x^3/coefficient of x^4 = -0/1 = 0.
x^4 = -3.
So x^2 = + or - sqrt(-3)^(1/2) , two roots
Fro x^2 = +sqrt(-3), we get:
x1 = + sqrt(-3)^(1/4)
x2 = - sqrt(-3)^(1/4)
From x^2= - sqrt(-3)^(1/4)
x3 = +i*sqt(-3)^(1/4) and
x4 = -i sqrt(-3)^(1/4), where i = (-1)^(1/2)
So, x1+x2+x3+x4 = 0
We'll use Viete relations.
For example, if the equation is :
a*x^4 + b*x^3 + c*x^2 + d*x + e=0
x1 + x2 + x3 + x4=-b/a
We'll indentify the coefficients from the given equation: a=1 and b=0
x1 + x2 + x3 + x4 = 0/1
x1 + x2 + x3 + x4=0