The interval(s) of x which satisfy the inequality (1−3x)7(1+5x)4(x+5)6(x2−1)(x−6)3(1−2x)4>0 is/are
A
(−5,−1)
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B
(−15,13)
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C
(1,6)
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D
(−∞,−5)
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Solution
The correct options are B(−15,13) C(1,6) (1−3x)7(1+5x)4(x+5)6(x2−1)(x−6)3(1−2x)4>0 Making coefficient of x positive ⇒(3x−1)7(1+5x)4(x+5)6(x2−1)(x−6)3(2x−1)4<0 Sign changes only for odd powers ⇒(3x−1)7(1+5x)4(x+5)6(x−1)(x+1)(x−6)3(2x−1)4<0