Question:
if alpha and beta are the zeroes of the polynomial x2 7x 3, then the value of (alpha - beta)2 is
Answer:
Given polynomial is
x2 + 7x + 3
Given α and β are zeroes of this polynomials then
α + β = -7
α * β = 3
Now
(α - β)2 = (α + β)2 - 4*α * β
= (-7)2 - 4*(-7)*3
= 49 + 84
= 133
=> α - β = √133
So α - β = √133
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