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Question

The interval(s) of x which satisfy the inequality (13x)7(1+5x)4(x+5)6(x21)(x6)3(12x)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)
(13x)7(1+5x)4(x+5)6(x21)(x6)3(12x)4>0
Making coefficient of x positive
(3x1)7(1+5x)4(x+5)6(x21)(x6)3(2x1)4<0
Sign changes only for odd powers
(3x1)7(1+5x)4(x+5)6(x1)(x+1)(x6)3(2x1)4<0

Critical points are
{5,1,15,13,12,1,6}


x(1,13)(1,6){15}

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