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I need help with - Complex numbers and quadratic equations - JEE Main-12

The number of integral values of m for which the equation \left ( 1+m^{2} \right )x^{2}-2\left ( 1+3m \right )x+\left ( 1+8m \right )=0 has no real root is : 


 

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    infinitely many

  • Option 4)

    3

 
Answers (1)
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Given equation is 

\left ( 1+m^{2} \right )x^{2}-2\left ( 1+3m \right )x+\left ( 1+8m \right )=0

given eq. has no real root

\Rightarrow D<0

\Rightarrow4\left ( 1+3m \right )^{2}-4\left ( 1+m^{2} \right )\left ( 1+8m \right )<0

\Rightarrow 4(1+6m+9m^2)-4(1+8m+m^2+8m^3)<0

\Rightarrow -8m(2m-1)^{2}<0

Infinite value of m satisfies this. 


Option 1)

1

Option 2)

2

Option 3)

infinitely many

Option 4)

3

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