For the quadratic equation ax2+bx+c+0, find the condition that

(i) one root is reciprocal of other root

(ii) one root is m times the other root

(iii) one root is square of the other root

(iv) one root is nth power of the other root

(v) the roots are in the ratio m:n

Given, quadratic equation = ax2 + bx + c

i) one root is reciprocal of other root

Let one root be p so the other root of the quadratic equation be .

So, sum of roots  = p +  =

and product of roots =

or c = a

Hence, for c = a, one root of the given quadratic equation will be reciprocal of the other root.

ii) one root is m times the other root

Let one root be p so the other root of given quadratic equation be pm.

So, sum of roots  = p + pm  =

p (1+m)  =

p  = .... (1)

and product of roots =

.... (2)

On solving (1) and (2), you will get the required condition.

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