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  • Solve this problem - Complex numbers and quadratic equations - JEE Main-3

Let f\left ( x \right )= x^{2}-x+a . Then the values of 'a' for which f\left ( x \right )= 0 have real and distinct roots are 

  • Option 1)

    a\leq \frac{1}{4}

  • Option 2)

    a< \frac{1}{4}

  • Option 3)

    a> \frac{1}{4}

  • Option 4)

    a\geq \frac{1}{4}

 

Answers (1)

best_answer

For x^{2}-x+a=0  to have real and distinct roots

D> 0\Rightarrow 1-4a> 0\Rightarrow a< \frac{1}{4}

 

Quadratic Expression Graph when a> 0 & D > 0 -

Real and distinct roots of

f\left ( x \right )= ax^{2}+bx+c

& D= b^{2}-4ac

- wherein

 

 


Option 1)

a\leq \frac{1}{4}

This is incorrect

Option 2)

a< \frac{1}{4}

This is correct

Option 3)

a> \frac{1}{4}

This is incorrect

Option 4)

a\geq \frac{1}{4}

This is incorrect

Posted by

prateek

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