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Question
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.
Solution
It is given that `y=1` is a root of the equation `ay^2+ay+3=0`
∴`axx(1)^2+axx1+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`
⇒`1+1+b=0`
⇒`b+2=0`
⇒`b=-2`
∴`ab=(-3/2)xx(-2)=3`
Hence, the value of ab is 3.
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