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

Question

Aicharya · 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.

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…