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CAT 1990 Question-5




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)





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