Official solution
(1 + m2
)x2
-- 2(1 + 3m)x + (1 + 8m) = 0
Given equation has no real solution,
\[ \therefore \] Discriminant (D) < 0
\[ \Rightarrow \] 4(1 + 3m)2 - 4(1 + m2)(1 + 8m) < 0
\[ \Rightarrow \] 4[9m2 + 6m + 1 - 8m - 1 - 8m3 - m2] < 0
\[ \Rightarrow \] -8m3 + 8m2 - 2m < 0
\[ \Rightarrow \] -2m(4m2 - 4m + 1) < 0
\[ \Rightarrow \] m(2m - 1)2 > 0
\[ \therefore \] m > 0 and m \[ \ne \] \[{{1 \over 2}}\]
So we can say number of integral values of m are infinitely
many.