Question 766202
The roots of the quadratic equation a*x^2 + b^x + c = 0 are

1) {{{(-b + sqrt(b^2 - 4*a*c))/(2*a)}}}

and

2) {{{(-b - sqrt(b^2 - 4*a*c))/(2*a)}}}

If they are reciprocals of each other

{{{(-b + sqrt(b^2 - 4*a*c))/(2*a) = (2*a) / (-b - sqrt(b^2 - 4*a*c))}}}

Cross multiplying:

{{{b^2 - (b^2 - 4*a*c) = 4*a^2}}}

{{{4*a*c = 4*a^2}}}

Dividing both sides by 4*a 

We can do because we know that a cannot be 0 for a quadratic)

{{{c = a}}}

Hope you got it. Let me know if it is not clear :)

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