Given equation is (1+m2)x2−2(1+3m)x+(1+8m)=0 ∵ equation has no real solution ∴D<0 ⇒4(1+3m)2<4(1+m2)(1+8m) ⇒1+9m2+6m<1+8m+m2+8m3 ⇒8m3−8m2+2m>0 ⇒2m(4m2−4m+1)>0⇒2m(2m−1)2>0 ⇒m>0 and m≠
1
2
[∵
1
2
is not an integer ] ⇒ number of integral values of m are infinitely many.