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Q.) The roots of the equation ${ aX }^{ 2 }+3X+6=0$ will be reciprocal to each other if the value of a is

1)3

2)4

3)5

4)6

Solution :

The product of the roots in the quadratic equation ${ aX }^{ 2 }+bX+c=0$ is given by

product of the roots = $\frac{c}{a}$

Let the roots of the equation ${ aX }^{ 2 }+3X+6=0$ be $\alpha $ and $\frac { 1 }{ \alpha } $ (as they are reciprocal to each other)

Product of the roots = $\frac { 6 }{ a } $

=> $\alpha $ X $\frac { 1 }{ \alpha } $ = $\frac { 6 }{ a } $

=> 1 = $\frac { 6 }{ a } $

=> a = 6.

Hence , Option(4)