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 = ax^{2} + 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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