If one of the s of the quadratic equation ax^2+bx+c=0 be is n times the other, then b^n is equal to
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question ask one of the root of quadratic n times then other
let one root r then other root is r.n
now use quadratic properties
r+r.n=-b/a-------(1)
r^2.n=c/a-------(2)
from equation (1)
r (1+n)=-b/a
and equation (2)
r^2=c/a.n
now put r value in r (1+n)=-b/a
( c/a.n) (1+n)=-b/a
b=-c (1+1/n)
take n power on both side
b^n=(-c)^n. (1+1/n)^n
let one root r then other root is r.n
now use quadratic properties
r+r.n=-b/a-------(1)
r^2.n=c/a-------(2)
from equation (1)
r (1+n)=-b/a
and equation (2)
r^2=c/a.n
now put r value in r (1+n)=-b/a
( c/a.n) (1+n)=-b/a
b=-c (1+1/n)
take n power on both side
b^n=(-c)^n. (1+1/n)^n
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