If the zeros of the polynomial f(x)=x3−3x2+x+1 are (a-b), a and (a+b), find a and b.
As the the coefficient of highest power x3 is1, if three roots are α,βandγ, we have
Now let us compare coefficients of similar powers on each side.
First comparing the sum of roots from the coefficient of x2, we have
Also, coefficients of x give us the sum of the product of zeros
Further, products of roots is (a−b)a(a+b)=1.
Hence, a=1 and b=±√
Note that the two values of b give the same set of roots.