If 1 is a root of the equation ay^{2} + ay + 3 = 0 and y^{2} + y + b = 0 then find the value of ab.

Given that y = 1 is a root of the equation ay^{2} + ay + 3 = 0

a.1^{2} + a.1 + 3 = 0

a + a + 3 = 0

2a + 3 = 0

a = - 3/2

Also y = 1 is a root of the equation y^{2} + y + b = 0

1^{2} + 1 + b = 0

2 + b = 0

b = - 2

Thus the value of ab = 3

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