Find the condition that one root of the quadratic equation aX²+bX+c=0 shall be n times the other,where n is a positive integer.

let the roots be k and l. so x= k or l. so k= nl. sum of roots = -b\a ie.. (n+1)l. products of roots= c\a ie. nl^2=c\a.

now divide both sum and product. 

so (n+1)\n=-bl\c

Hi Halak,

Let p, np be the roots of the given QE.

So p+np = -b/a, and np² = c/a

Or (n+1)p = -b/a or p = -b/a(n+1)

So n[-b/a(n+1)]² = c/a

or nb²/a(n+1)² = c

or nb² = ac(n+1)²

Which will give acn² + (2ac-b²)n + ac = 0, which is the required condition.

Hope that helps.

Best Regards,

Ashwin (IIT Madras).