if one root of ax2+bx+c=0 is equal to nthpower of other than b is - Maths - Mathematical Induction and Binomial Theorem

Question

if one root of ax2 +bx+c=0 is equal to
nthpower of other than b is

Rahul Raj · Accepted Answer

dear student

ax2+bx+c=0let the roots be α and αn as one root is nth power of othersum of roots=-ba α +αn =-baproduct of roots=ca α *αn =caαn+1=caα=ca1n+1from the first equationα +αn =-bab=-a(α +αn )=-aα(1 +αn-1 )=-aca1n+11+can-1n+1

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if one root of ax2 +bx+c=0 is equal to nthpower of other than b is

if one root of ax² +bx+c=0 is equal to n^thpower of other than b is