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Real value(s) of 'a' for which both roots of  ax^{2}+2x-1=0  are real is

 

Option: 1

\left ( -\infty ,1 \right )


Option: 2

\left( -\infty,1 \right ]


Option: 3

(-\infty,1]-\{0\}


Option: 4

none of these


Answers (1)

best_answer

For real roots D> 0 \: or\: D=0

\Rightarrow D\geq 0\\

\Rightarrow 2^{2}-4(a)(-1)\geq 0\\

\Rightarrow 4+4a\geq 0\\

\Rightarrow 4a\leq 4\\

\Rightarrow a\leq 1

a\: \epsilon \: \left ( -\infty,1 \right ]

Also note that for a=0, the equation will not be quadratic and will not have 2 roots, so will be excluded .

\therefore a\: \epsilon \left ( -\infty,1 \right ]-\{0\}

 

Posted by

sudhir.kumar

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