The number of integral values of m for which the equation, 1 + m 2 x 2 - 2 1 + 3 m x + 1 + 8 m = 0 has no real root, is

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TestHub · Accepted Answer

Since the given equation has no real solution.
$\Rightarrow D < 0$
$\Rightarrow 4 {(1 + 3 m)}^{2} - 4 \times (1 + m^{2}) (1 + 8 m) < 0$
$\Rightarrow (1 + 9 m^{2} + 6 m) - (1 + 8 m + m^{2} + 8 m^{3}) < 0$
$\Rightarrow - 2 m {(2 m - 1)}^{2} < 0$
Clearly, for infinite values of $m$ given condition is true.

Mathematics - Quadratic Equation Question with Solution | TestHub

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