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  • If roots of the equation <img alt="\left({ }^m C_0+{ }^m C_1 \ldots \ldots . .{ }^m C_m\righ

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 \ldots \ldots\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

Roots are real if Discriminant is greater than or equal to 0

\begin{aligned} & \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 \end{aligned}

minimum value of n – m = 3

Posted by

jitender.kumar

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