The number of integral values of

Question:

The number of integral values of $m$ for which the equation

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

has no real root is :

  1. infinitely many

  2. 2

  3. 3

  4. 1


Correct Option: 1

Solution:

$D<0$

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

$\Rightarrow \mathrm{m}(2 \mathrm{~m}-1)^{2}>0 \Rightarrow \mathrm{m}>0$

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