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Find the set of all x for which (1987, 3...

Find the set of all `x` for which (1987, 3M) `(2x)/(2x^2+5x+2)>1/(x+1)`

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We have `(2x)/((2x^(2)+5x+2))ge1/((x+1))`
`implies(2x)/((x+2)(2x+1))-1/((x+1))gt0`
`implies((2x^(2)+2x)-(2x^(2)+5x+2))/((x+2)(x+1)(2x+1))gt0`
`implies-((3x+2))/((x+2)(x+1)(2x+1))gt0`
or `((3x+2))/((x+2)(x+1)(2x+1))lt0`
The critical points are `(-2),(-1),(-2/3),(-1/2)`.
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ARIHANT MATHS-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  3. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

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  17. The smallest value of k, for which both the roots of the equation, x^2...

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  20. Conder the function f(x)=1+2x+3x^2+4x^3 Let the sum of all distinct ...

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  21. Let alpha and beta be the roots of x^2-6x-2=0 with alpha>beta if an=al...

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