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  • If roots of the equation<img alt="\left({ }^{m} C_{0}+{ }^{m} C_{1} \ldots \ldots . .{ }^{m} C_{m}\right) x^{2}-\left({ }^{n} C_{0}+{ }^{n} C_{2}+{ }^{n} C_{4} \cdots

If roots of the equation\left({ }^{m} C_{0}+{ }^{m} C_{1} \ldots \ldots . .{ }^{m} C_{m}\right) x^{2}-\left({ }^{n} C_{0}+{ }^{n} C_{2}+{ }^{n} C_{4} \cdots \cdots ..\right) x+ \left({ }^{n} C_{1}+{ }^{n} C_{3}+{ }^{n} C_{5} \cdots \cdots ..\right)=0  are real , find minimum value of n-m.

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

-1


Answers (1)

best_answer

(C) Roots are real if

\left(2^{n-1}\right)^{2}-4\left(2^{m}\right) 2^{n-1} \geq 0 \\

2^{2 n-2}-2^{m+n+1} \geq 0 \\

 2 n-2 \geq m+n+1 \\

 n-m \geq 3

Minimum value of n=m=3

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