2s2 - (1 + 22)s + 2.


By splitting the middle term


2s2 - (1 + 2√2) s + √2 = 0


2s2 - s - 2√2s + √2 = 0


s (2s - 1) - √2(2s - 1) = 0


(2s - 1)(s - √2) = 0


s = 1/2, √2


Verification:


Sum of the zeroes = - (coefficient of x) ÷ coefficient of x2


α + β = - b/a


(1/2) + (√2) = - {(1 + 2√2)}/2


= - (1 + 2√2)/2 = - (1 + 2√2)/2


Product of the zeroes = constant term ÷ coefficient of x2


α β = c/a


(1/2)(√2) = √2/2


1/√2 = 1/√2


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