Question

Very-Short-Answer Questions

If 1 is a root of the equation $a{y}^2+ay+3=0$ and $y^2+y+b=0$ then find the value of ab. [CBSE 2012]

Answer 1

It is given that y = 1 is a root of the equation $a{y}^2+ay+3=0$.
$$\begin{gathered} \therefore a\times {\left(1\right)}^2+a\times 1+3=0 \\ \Rightarrow a+a+3=0 \\ \Rightarrow 2a+3=0 \\ \Rightarrow a=-\frac{3}{2} \end{gathered}$$

Also, y = 1 is a root of the equation $y^2+y+b=0$.
$$\begin{gathered} \therefore {\left(1\right)}^2+1+b=0 \\ \Rightarrow 1+1+b=0 \\ \Rightarrow b+2=0 \\ \Rightarrow b=-2 \end{gathered}$$

$\therefore ab=\left(-\frac{3}{2}\right)\times \left(-2\right)=3$

Hence, the value of ab is 3.