The range of α for which the points (α,α+2) and 3α2,α2 lie on opposite sides of the line 2x+3y−6=0

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(−∞,−2)

(0,1)

(−∞,−2)∪(0,1)

(−∞,1)∪ (2,∞)

answer is C.

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Detailed Solution

Points lie on opposite sides of the line⇒L11L22<0⇒5α(3α+3α2−6)<0→α(α+2)(α−1)<0⇒α∈(−∞,−2)∪(0,1)

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