Consider two functions `y=f(x) and y=g(x)` defined as
f(x)=`{[a x^2 +b, 0lexle1],[ bx + 2b, 1ltxle3],[(a-1)x + 2c - 3 , 3ltxle4]}` And `g(x)={[c x + d , 0le x le 2],[a x+3-c ,2ltxlt3],[x^2+b+1,3lexle4]}`
Let `f` be differentiable at `x=1a n dg(x)` be continuous at `x=3.` If the roots of the quadratic equation `x^2+(a+b+c)alphax+49(k+kalpha)=0` are real distinct for all values of `alpha` then possible value of `k` will be
a)`k in (-1,0)`
b). `k in (oo,0)`
c). `k in (1,5)`
d). `k in (-1,1)`