If 2x³ + ax² + bx - 2 leaves the remainders 7 and 0 when divided by (2x - 3) and (x + 2), respectively, then the values of a and b are respectively:

Solution (By Examveda Team)

$$\eqalign{ & f\left( x \right) = 2{x^3} + a{x^2} + bx - 2 \cr & x + 2 = 0 \cr & x = - 2 \cr & f\left( { - 2} \right) = 2{\left( { - 2} \right)^3} + a{\left( { - 2} \right)^2} + b\left( { - 2} \right) - 2 = 0 \cr & \Rightarrow - 16 + 4a - 2b - 2 = 0 \cr & \Rightarrow 4a - 2b - 18 = 0 \cr & {\text{Now go through option - }} \cr & {\text{from option A}} \cr & 4 \times 3 - 2\left( { - 3} \right) - 18 = 0 \cr & 0 = 0{\text{ satisfy}} \cr} $$