Question
If one root of the quadratic equation ax2 + bx + c = 0 is equal to the nth power of the other root, then the value of (acn)1n+1 + (anc)1n+1
Answer: Option B
:
B
Let α, αn be two roots,
Then α+αn = -ba, ααn =ca
Eliminating α, we get(ca)1n+1 +(ca)nn+1 = -ba
⇒ a.a−1n+1.c1n+1 +a.a−nn+1.cnn+1 = -b
or(anc)1n+1 + (acn)1n+1 = -b
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:
B
Let α, αn be two roots,
Then α+αn = -ba, ααn =ca
Eliminating α, we get(ca)1n+1 +(ca)nn+1 = -ba
⇒ a.a−1n+1.c1n+1 +a.a−nn+1.cnn+1 = -b
or(anc)1n+1 + (acn)1n+1 = -b
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