Find the number of integral values of k for which e^ ^2-2 +1+ 3 and e^ - ( ^2-2 +1 )+ 2 , where R- 1 are the roots of the equation x^2-(3 k+1) x+3 k^2-k+2=0 .

Step-by-step solution

aligned Product of roots & =3 k^2-k+2=e^ 3+ 2 =6 3 k^2-k-4 & =0 3 k^2-4 k+3 k-4 & =0 (k+1)(3 k-4) & =0 k & =-1, k= 4 3 Sum of roots & =3 k+1=3 e^ ^2-2 +1 +2 e^ - ( ^2-2 +1 ) aligned k=-1 not satisfy given relation So, number of integral value of k is zero.