The equations 2x2+bx+(c+1)=0 where b,c∈Q and x2+3x−5=0 have a common  root, then the value of b−c is

The given equations are 2x2+bx+(c+1)=0 and x2+3x−5=0 Since, x2+3x−5=0 have irrational roots.  since ∆ is not a perfect square Here one  root is common ⇒ the other root also common because coefficients are rational.  (The roots of a quadratic equation occurs in conjugate surds if the                                                                                                                           coefficients are rationals)⇒21=b3=c+1−5⇒b=6,c=−11⇒b−c=6+11=17Therefore, The correct answer is(4).