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[Solved] Inequality value

 
Inequalities
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June 15, 2021 12:26 pm
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(@armor)
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Given (m+1)x^2-2(m-1)x+3(m-1)<0,  find all real values of m such that the inequality has no solution.

 

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June 15, 2021 12:27 pm
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Staff 
(@armor)
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The inequality has no solution if and only if

\small \Delta =4(m-1)^2-12(m+1)(m-1)\leq 0

\small m+1>0

\small \Rightarrow

\small m^2+m-2\geq 0

\small m+1>0

\small \Rightarrow

\small m\leq -2   or  \small m\geq 1

\small m>-1

\small \Rightarrow m\geq 1.

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