If the zeroes of the polynomial x3-3x2+x+1 are a-b,a and a+b ,find the values of the a and b

If the zeroes of the polynomial x3-3x2+x+1 are a-b,a and a+b ,find the

1.	If the zeroes of the polynomial x3-3x2+x+1 are a-b,a and a+b ,find the values of the a and b
Answer» {tex}\\begin{array}{l}let\\;\\alpha,\\beta,\\gamma\\;are\\;zeros\\\\hen\\;\\alpha+\\beta+\\gamma=-\\frac{-3}1=3\\\\or\\;a-b+a+a+b=3\\\\3a=3\\;so\\;\\;a=1\\\\\\alpha\\beta\\gamma=-\\frac11=-1\\\\so\\;a(a-b)(a+b)=-1\\\\a(a^2-b^2)=-1\\\\1(1-b^2)=-1\\\\b^2=2\\\\b=\\pm\\sqrt2,a=1\\end{array}{/tex} a=1 and b= root 2