CAN YOU SOLVE THIS ??? #
If one root of the quadratic equation a +bx+c=0 is power of the other.Then find the value of )^ +( c)^ +b.
The answer is 0.
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1 solution
Given equation
ax^2+bx+c
Let the roots be p and q
p+p^n=-b/a and p.p^n=(c/a)^1/n+1
a(c^1/n+1 / a^1/n+1) + a(c^n/n+1 / a^n/n+1) + b=0
c^1/n+1 . a^1-1/n+1 + c^n/n+1 . a^1-n/n+1 + b=0
=>c^1/n+1 . a^n/n+1 + c^n/n+1 . a^1/n+1 + b=0
=>(a^n.c)^1/n+1 + (ac^n)^1/n+1 + b=0
Therefore (a^n.c)^1/n+1 + (ac^n)^1/n+1 + b=0