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# CAT 1990 Question-5

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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)