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If the zeros of the polynomial x3 – 3x2 + x + 1 are (a ‒ b), a and (a + b), find the values of a and b
It is given in the question that the roots of the given polynomial are (a – b), a and (a + b)
Now by comparing the given polynomial with Ax3 + Bx2 + Cx + D, we get:
A = 1, B = - 3, C = 1 and D = 1
Now,
(a – b) + a + (a + b) =
3a = -
a = 1
Also, we have:
(a – b) × a × (a + b) =
a (a2 – b2) =
1 (12 – b2) = - 1
1 – b2 = - 1
b2 = 2
b =
Hence, a = 1 and b =