Question

If y = 1 is a common root of the equations \[a y^2 + ay + 3 = 0 \text { and } y^2 + y + b = 0\], then ab equals

Options

• 3

• -7/2

• 6

• -3

Answer 1

Since, y = 1 is a root of the equations \[a y^2 + ay + 3 = 0\].

So, it satisfies the given equation.

\[\therefore a \left( 1 \right)^2 + a\left( 1 \right) + 3 = 0\]

\[ \Rightarrow 2a + 3 = 0\]

\[ \Rightarrow a = - \frac{3}{2} . . . (1)\]

Since, y = 1 is a root of the equations  \[y^2 + y + b = 0\].

So, it satisfies the given equation. 

\[\therefore \left( 1 \right)^2 + \left( 1 \right) + b = 0\]

\[ \Rightarrow 2 + b = 0\]

\[ \Rightarrow b = - 2 . . . (2)\] 

From (1) and (2),

\[ab = \left( - \frac{3}{2} \right)\left( - 2 \right)\]

\[ = 3\]

Thus, ab is equal to 3.