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Let $f\left ( x \right )= \left ( -1+a \right )x^{2}+\left ( 2a \right )x+a$ , then the value of $'a'$ for which $f\left ( x \right )\leq 0$ $\forall$ $x\, \epsilon \, R$ is

Option 1)
$\left ( -\infty ,0 \right )$

Option 2)
$(-\infty,1]$

Option 3)
$(-\infty,0]$

Option 4)
$\left ( -\infty,\infty \right )$

Answers (1)

best_answer

$f\left ( m \right )\leq 0\; n\epsilon R$ if $-1+a< 0$

and $D\leq 0$

$\Rightarrow a< 1\; \; \; \; \; \; and\; \; \; \; \; \; 4a^{2}-4\left ( a-1 \right )\left ( a \right )\leq 0$

$\Rightarrow a< 1\; \; \; \; \; \; and\; \; \; \; \; \; 4a^{2}-4a^{2}+4a\leq 0$

$\Rightarrow a< 1\; \; \; \; \; \; and\; \; \; \; \; \;a\leq 0$

$\Rightarrow a\leq 0$ will be answer

Option 1)

$\left ( -\infty ,0 \right )$

This is incorrect

Option 2)

$(-\infty,1]$

This is incorrect

Option 3)

$(-\infty,0]$

This is correct

Option 4)

$\left ( -\infty,\infty \right )$

This is incorrect

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Aadil

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