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Tell me? - Complex numbers and quadratic equations - JEE Main-2

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)
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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

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