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Maths-

General

Easy

Question

If roots of the eduation $open parentheses blank to the power of m end exponent C subscript 0 end subscript plus blank to the power of m end exponent C subscript 1 end subscript midline horizontal ellipsis blank to the power of m end exponent C subscript m end subscript close parentheses x to the power of 2 end exponent plus open parentheses blank to the power of n end exponent C subscript 0 end subscript plus blank to the power of n end exponent C subscript 2 end subscript plus blank to the power of n end exponent C subscript 4 end subscript midline horizontal ellipsis close parentheses x plus open parentheses blank to the power of n end exponent C subscript 1 end subscript plus blank to the power of n end exponent C subscript 3 end subscript plus blank to the power of n end exponent C subscript 5 end subscript midline horizontal ellipsis close parentheses equals 0$ are real, then find the minimum value of n –m.

1
2
3
-1

The correct answer is: 3

Roots are real if
$table row cell open parentheses 2 to the power of n minus 1 end exponent close parentheses to the power of 2 end exponent minus 4 open parentheses 2 to the power of m end exponent close parentheses 2 to the power of n minus 1 end exponent greater or equal than 0 end cell row cell 2 to the power of 2 n minus 2 end exponent minus 2 to the power of m plus n plus 1 end exponent greater or equal than 0 end cell row cell 2 n minus 2 greater or equal than m plus n plus 1 end cell row cell n minus m greater or equal than 3 end cell end table$
Minimum value of n – m = 3.

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