If n is an even number and α, β are the root of the equation x2 + ax + b = 0 and βα is a root of eqn xn + 1 + (x+1)n = 0, and f(x) = x2n + anxn + bn, then which of the following is (are) necessarily true?
(a) f(αn) = 0
(b) f(α) = 0
(c) f(β) = 0
(d) f(βn) = 0
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1 Answers
62\\\left( \frac{\beta}{\alpha}\right)^n+1+\left(\frac{\beta}{\alpha}+1\right)^n=0 \\ \beta^n+\alpha^n+\left({\beta}+{\alpha}\right)^n=0
now see that a = -α-β
and divide f(x) by x^n
then can you figure out something?
