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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).
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