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If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b
Asked by pramodmahto80 | 15 Dec, 2022, 04:30: PM Expert Answer
P(x) = x3 - 3x2 + x + 1
It is given that a-b, a and a+b are the zeroes of this polynomial P(x)
Using the relation between zeroes and coefficients, we have
(a-b)+a+(a+b) = -(-3)/1
3a = 3
Therefore, a = 1

Also, (a-b)a(a+b) = -1
i.e. a(a2 - b2) = -1
i.e. 1 - b2 = -1
i.e. b2 = 2
Therefore, b = sqrt{2}, -sqrt{2}
Answered by Renu Varma | 15 Dec, 2022, 04:54: PM

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