If the zeroes of the polynomial f(x)=x^3-3x^2+x+1 are (a-b),a and(a+b),find a and b.

If the zeroes of the polynomial f(x)=x^3-3x^2+x+1 are (a-b),a and(a+b)

1.	If the zeroes of the polynomial f(x)=x^3-3x^2+x+1 are (a-b),a and(a+b),find a and b.
Answer» f(x) = x3 - 3x2 + x + 1It is given that a - b, a and a + b are the zeroes of f(x).Now, Sum of the zeroes ={tex} - \\frac { \\text { Coeff. of } x ^ { 2 } } { \\text { Coeff. of } x ^ { 3 } }{/tex}⇒ a - b + a + a +b =\xa0{tex}- \\frac { - 3 } { 1 } {/tex}⇒ 3a = 3\xa0⇒ a = 1and, Product of zeros ={tex} - \\frac { \\text { Constant term } } { \\text { Coeff. of } x ^ { 3 } }{/tex}⇒ (a -b )(a) (a + b) ={tex} - \\frac { 1 } { 1 }{/tex}⇒ a(a2\xa0- b2) = -1⇒ 1 - b2\xa0= -1 (∵ a = 1)⇒b2\xa0= 2\xa0⇒\xa0b =\xa0{tex} \\pm \\sqrt { 2 }{/tex}Hence the value of a = 1 and b = {tex} \\pm \\sqrt { 2 }{/tex}