Question

When the roots of a quadratic equation are reciprocal of each other?

Answer 1

HEY MATE

HERE IS UR ANSWER

:- let the roots of given quadratic equation be a & 1/a

so, product of zeroes = a * 1/a = 1

i.e c/a

Thus a = c is tge required condition.

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Answer 2

Let r1,r2 be the two solutions of the quadratic. Then we have

ax2+bx+c=a(x−r1)(x−r2)=ax2−a(r1+r2)x+ar1r2

so that c=ar1r2. Since one solution is the reciprocal of the other, we have r1r2=1, so that a=c. Hence, the roots are reciprocals of one another only when a=c.