.


By splitting the middle term


y2 + y - 5 = 0


2y2 + 3√5y - 10 = 0


2y2 + (4√5y - √5y) - 10 = 0


2y2 + (4√5y - √5y) - 10 = 0


2y(y + 2√5) - √5(y + 2√5) = 0


(y + 2√5)(2y - √5) = 0


y = - 2√5, √5/2


Verification:


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


α + β = - b/a


(- 2√5) + (√5/2) = - (3√5)/2


= - 3√5/2 = - 3√5/2


Product of the zeroes = constant term ÷ coefficient of x2


α β = c/a


(- 2√5)(√5/2) = - 5


- 5 = - 5


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