Roots and polynomials
If z is an n-th term of 1, show taht 1+z+z^2+z^3+....+z^n-1=0.
Solve the equation with n=5 and hence factorize 1+z+z^2+z^3+z^4 into linear factors with complex coefficient and then into quadratic factors with real coefficients.© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/algebra/roots-and-polynomials-201
<br> So we have a+b=1, ab+2=1 or ab=-1
<br> Thus a and b satisfies the quadratic equation x^2-x-1=0
<br> By quadratic formula, we have a=(1+sqrt(5))/2, b=(1-sqrt(5))/2