Q60 / 90 · JEE Main 2019 (08 Apr Shift 2) · Mathematics

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

A
$2$
B
$3$
Correct answer
C
Infinitely many
D
$1$

Solution

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.

Hence, the correct answer is option: 'C'.

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