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Continuity in an Interval

lf 1, -1, 2...

Question

lf $1, - 1, 2$ are the roots of $x^{3} + A x^{2} + B x + C = 0$ , then the ascending order of $A, B, C$ , is

A, B, C

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B, A, C

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C, B, A

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C, A, B

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Solution

The correct option is B $A, B, C$
As $1, - 1, 2$ are roots of $x^{3} + A x^{2} + B x + c = 0$
Gives
$S_{1} = 1 - 1 + 2 = - A \Rightarrow A = - 2 S_{2} = 1. (- 1) + 1.2 + (- 1) .2 = B \Rightarrow B = - 1 S_{3} = (1) (- 1) (2) = - C \Rightarrow C = 2$
Hence
$C > B > A$

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