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The values of $'a'$ for which $-x^{2}+x-a< 0$ $\forall$ $x\; \epsilon \; R$ is

Option 1)
$a> -2$

Option 2)
$a> -1$

Option 3)
$a> \frac{1}{4}$

Option 4)
$a> 0$

Answers (1)

best_answer

Coeff of $x^{2}=-1< 0$ only required more is $D< 0\, \Rightarrow \: 1-4a< 0\: \Rightarrow \, a> \frac{1}{4}$

$\therefore$ Option (C)

Value of quadratic expression as negative. -

$ax^{2}+bx+c$ will be always negative, for all $x\epsilon R$ , If $a< 0$ & $b^{2}-4ac< 0$ $\left ( Where\; a,b,c\; \epsilon\; R \right )$

- wherein

So, graph of $y= ax^{2}+bx+c$ will be always below x-axis so $ax^{2}+bx+c= 0$ has no real roots.

Option 1)

$a> -2$

This is incorrect

Option 2)

$a> -1$

This is incorrect

Option 3)

$a> \frac{1}{4}$

This is correct

Option 4)

$a> 0$

This is incorrect

Posted by

Himanshu

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