Let and the roots of the quadratic equation x^2 -x( +1)+ =0 (0< <45^ ), and < . Then _ n=0 ^ ( ^n+ (-1)^n ^n ) is equal to

JEE Main Mathematics question

Let and the roots of the quadratic equation , and . Then is equal to

Answer: (B)

The equation factors as , so the roots are and ; for , , so and

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Question ID VK-014265