( x 3 + 6 x 2 + 1 2 x + 8 ) ( x + 1 ) 2 ( 8 x 3 + 3 6 x 2 + 5 4 x + 2 7 ) ( x − 1 ) 2 < 0
Find all the possible values of x .
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Nice solution! One can also solve this question in 10 sec by eliminating wrong options by trial and error.
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What if it was "Less Than or Equal To" Zero? What are we supposed to do about the denominators? Your help will be appreciated.
Nice work. An alternative approach is to multiply both sides of the inequality by (denominator) 2 , so the inequality remains unchanged and you are left with a polynomial.
May I know what app do you use to create this graph?
If it is positive? How to write the answer
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You can solve it the same way by looking at the graph that the author posted.
We can see that 1 is common in 3 options except 1st option, and when we put 1 as x the answer comes to be equal to 0 which is equal to 0. Hence instead of solving this question through wavy curve, we can just put and check for some values of x. Hope this helps you :)
Though this is not the perfect explanantion, this is the best method to obtain answer in less time in competitive exams.
It is called trial and error
Answer is incorrrect cause -1 should be excluded
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Relevant wiki: Wavy Curve Method
( x 3 + 6 x 2 + 1 2 x + 8 ) ( x + 1 ) 2 ( 8 x 3 + 3 6 x 2 + 5 4 x + 2 7 ) ( x − 1 ) 2 ( x 3 + 8 + 6 x ( x + 2 ) ) ( x + 1 ) 2 ( 8 x 3 + 2 7 + 1 8 x ( 2 x + 3 ) ) ( x − 1 ) 2 ( x 3 + 2 3 + ( 3 × x × 2 ) ( x + 2 ) ) ( x + 1 ) 2 ( 2 x 3 + 3 3 + ( 3 × 2 x × 3 ) ( 2 x + 3 ) ) ( x − 1 ) 2 ( x + 2 ) 3 ( x + 1 ) 2 ( 2 x + 3 ) 3 ( x − 1 ) 2 Roots of odd powers Roots of even powers < 0 < 0 < 0 < 0 = − 2 , − 1 . 5 = − 1 , 1
Since the inequality is only < 0 and not ≥ 0 or ≤ 0, we dont care about the roots of the denominators.
∴ x ∈ ( − 2 , − 1 . 5 )