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.  

Answer 1

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.