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If the zeroes of the polynomial x^3 – 3x^2 + x + 1 are a – b, a, a + b, find a and b.

Q3  If the zeroes of the polynomial x^3 - 3 x^2+ x +1  are a – b, a, a + b, find a and b.

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S Sayak

x^3 - 3 x^2+ x +1

The roots of the above polynomial are a, a - b and a + b

Sum of the roots of the given plynomial = 3

a + (a - b) + (a + b) = 3

3a = 3

a = 1

The roots are therefore 1, 1 - b and 1 + b

Product of the roots of the given polynomial = -1

1 x (1 - b) x (1 + b) = - 1

1 - b2 = -1

b- 2 = 0

b=\pm \sqrt{2}

Therefore a = 1 and b=\pm \sqrt{2}.

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