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Find the condition that one root of the quadratic equation aX 2 +bX+c=0 shall be n times the other,where n is a positive integer.

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.

Grade:10

2 Answers

sha swa
14 Points
10 years ago

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

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

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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