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Q.

If S is the set of all real  x, such that 2x−12x3+3x2+x is positive then S contains

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a

−∞,−32

b

−31,−14

c

−14,12

d

12,3

answer is A, D.

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Detailed Solution

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f(x)=2x−12x3+3x2+x=2x−1x(2x+1)(x+1)
Critical points are x=12,0,−12,−1
Question Image
f(x)>0
⇒x∈(−∞,−1)∪−12,0∪12,∞

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If S is the set of all real  x, such that 2x−12x3+3x2+x is positive then S contains