Question

If 1 is a root of the equations $a{y}^2+ay+3=0$ and $y^2+y+b=0$ then ab equals :

• A. 3
• B.
  
• C. 6
• D. -3

Answer 1

The correct option is A 3

The given equations are $a{y}^2+ay+3=0$ and $y^2+y+b=0$
Given, 1 is the roots of both the equations
Therefore, y =1 will satisfy both these equations.
Putting y =1 in $a{y}^2+ay+3=0$, we get
$a(1{)}^2+ax1+3=0$
$\therefore a+a+3=0$
$\Rightarrow 2a+3=0$
$\Rightarrow 2a=-3$
$\Rightarrow a=-\frac{3}{2}......\left(1\right)$
Putting y =1 in $y^2+y+b=0$, we get
$(1{)}^2+1+b=0$
$\therefore 1+1+b=0$
$\Rightarrow 2+b=0$
$\Rightarrow b=-2......\left(2\right)$
$\therefore ab=-\frac{3}{2}\ast (-2)=3$ [Using (1) & (2) ]
Thus, the value of ab is 3.