If 2x3 + ax2 + bx - 2 leaves the remainders 7 and 0 when divided by (…

Question

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:

Accepted Answer

Option A. 3; -3. Answer & Solution Answer: Option A Solution: & f ( x ) = 2x^3 + ax^2 + bx - 2 & x + 2 = 0 & x = - 2 & f ( - 2 ) = 2 ( - 2 )^3 + a ( - 2 )^2 + b ( - 2 ) - 2 = 0 & - 16 + 4a - 2b - 2 = 0 & 4a - 2b - 18 = 0 & Now go through option - & from option A & 4 × 3 - 2 ( - 3 ) - 18 = 0 & 0…