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  • Help me answer: - Complex numbers and quadratic equations - JEE Main-3

The value of 'a' for which x^{2}+x+a= 0 have both roots negative is

  • Option 1)

    \left [ 0,\frac{1}{4} \right ]

  • Option 2)

    [0,\frac{1}{4})

  • Option 3)

    \left ( 0,\frac{1}{4} \right )

  • Option 4)

    (0,\frac{1}{4}]

 

Answers (1)

best_answer

\left ( i \right )\: D\geq 0\: \Rightarrow\: 1-4a\geq 0\: \Rightarrow \: a\geq \frac{1}{4}\cdots \cdots \left ( 1 \right )

\left ( ii \right )\: \frac{-b}{2a}< 0\: \Rightarrow \: \frac{-1}{2}< 0\: \Rightarrow \: a\, \epsilon \, R\cdots \cdots \left ( 2 \right )

\left ( iii \right )\: \frac{a}{1}> 0\: \Rightarrow \: a> 0\cdots \cdots \left ( 3 \right )

\left ( 1 \right )\cap \left ( 2 \right )\cap \left ( 3 \right )\: \Rightarrow \: a\, \epsilon \, (0,\frac{1}{4}]

\therefore Option (D)

 

Both roots of a Quadratic Equation are negative -

\frac{-b}{a}< 0,\frac{c}{a}> 0

D= b^{2}-4ac\geqslant 0

- wherein

ax^{2}+bx+c=0

is the quadratic equation

 

 


Option 1)

\left [ 0,\frac{1}{4} \right ]

This is incorrect

Option 2)

[0,\frac{1}{4})

This is incorrect

Option 3)

\left ( 0,\frac{1}{4} \right )

This is incorrect

Option 4)

(0,\frac{1}{4}]

This is correct

Posted by

Plabita

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