$$\begin{gathered} Thenumberof\mathrm{int}egralvaluesofmforwhichtheequation \\ (1+m^2)x^2-2(1+3m)x+(1+8m)=0has norealrootis: \end{gathered}$$

$\begin{array}{l}Given(m^2+1)x^2-2(1+3m)x+(1+8m)=0hasnorealrootsthenD<0\\ \Rightarrow 4{(1+3m)}^2-4(m^2+1)(1+8m)<0\\ \Rightarrow 1+9m^2+6m-m^2-8m^3-1-8m<0\\ \Rightarrow 8m^3-8m^2+2m>0\\ \Rightarrow 2m(4m^2-4m+1)>0\\ \Rightarrow m(2m-1)>0\\ \therefore m>0\\ Infinitelymanyvalues\end{array}$