The correct option is C 8
Δ=∣∣
∣∣11112313α∣∣
∣∣
=1(2α−9)−1(α−3)+1(3−2)
=2α−9−α+3+1
=α−5
For infinitely many solutions,
Δ=0
⇒α−5=0
⇒α=5
Now,
Δ1=∣∣
∣∣11512913β∣∣
∣∣
=1(2β−27)−1(β−9)+5(3−2)
=2β−27−β+9+5
=β−13
For infinitely many solutions,
Δ1=0
⇒β−13=0
⇒β=13
Hence, β−α=13−5=8