. . Zero Sum of all Coefficients Let P x ( ) = 0be a polynomial equation such that the sum of the coefficients is zero. What actually the sum of coefficients is?
The sum of coefficients is nothing but P ( ). The sum of all coefficients is zero means that P ( ) which says that is a root of P x ( ). The rest of the problem of solving the equation is easy. Example .
Solve the equation x The sum of the coefficients of the polynomial is . Hence is a root of the polynomial. To find other roots, we divide x by x − and get x as the quotient. Solving this we get and − as roots.
Thus , , − form the solution set of the given equation.