find the condition that the ratio between the roots of the eqn. ax2+bx+c=0 may be m:n.

Let the roots be my & ny

Therefore  sum of roots => my+ny = -b/a

(m+n)y = -b/a .......1

Product of roots=> my x ny = c/a

mny2=c/a .........2

Squaring (1), we get

(m+n)2  y= (-b/a )...........3

Dividing 3 by 2…………(y2 will be cancelled)

(m+n)2/mn = b2/a2 x a/c

ac(m+n)2 = b2mn.

Hence, the required condition is ac(m+n)2 = b2mn.

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