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If 1 is a root of the equation ay^(2)+ay...

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.

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The correct Answer is:
ab=3
Since 1 is a root of each of the equations `ay^(2)+ay+3=0` and `y^(2)+y+b=0,` we have
`axx(1)^(2)+axx1+3=0" and "1^(2)+1+b=0`
`impliesa+a+3=0" and "2+b=0impliesa=(-3)/(2)" and "b=-2.`
`:." "ab=((-3)/(2))xx(-2)=3.`
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