(a) The equation of given curve is y=ax3+bx2+cx+5......(i) ∵ Curve (i) passes through point P(−2,0), so −8a+4b−2c+5=0(ii) and curve (i) cuts the Y-axis at a point Q with gradient 3, so
dy
dx
|Q=3 ⇒3ax2+2bx+c|x=0⇒c=3.....(iii) ∵ Point Q have coordinates (0,5), so curve (i) passes through Q(0,5). From Eqs. (ii) and (iii), we have 8a−4b+1=0. Now, from the options c=3,a=−