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