If 1 is a root of the equations ay² + ay + 3 = 0 and ${\mathrm{y}}^2+\mathrm{y}+\mathrm{b}=0,$ then find the value of ab.

Given equation:  ${\mathrm{ay}}^2+\mathrm{ay}+3=0$  

Given root = 1

So, ${\mathrm{a}\left(1\right)}^2+\mathrm{a}\left(1\right)+3=0$ 

${2\mathrm{a}=-3}_{ }$ 

$\mathrm{a}=\frac{-3}{2}$ 

And, ${\mathrm{y}}^2+\mathrm{y}+\mathrm{b}=0$ 

 ${1+1+\mathrm{b}=0}_{ }$ 

b = - 2 

∴ ${\mathrm{ab}=-\frac{3}{2}}_{ }{(-2)=3}_{ }$