The minimum value of (x - 2)(x - 9) is?

A. $$ - \frac{{11}}{4}$$

B. $$\frac{{49}}{4}$$

C. 0

D. $$ - \frac{{49}}{4}$$

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & \left( {x - 2} \right)\left( {x - 9} \right) \cr & = {x^2} - 9x - 2x + 18 \cr & = {x^2} - 11x + 18 \cr & = a{x^2} + bx + c = 0 \cr & {\text{For minimum value}} \cr & = \frac{{4ac - {b^2}}}{{4a}} \cr & = \frac{{4 \times 1 \times 18 - {{\left( { - 11} \right)}^2}}}{{4 \times 1}} \cr & = \frac{{72 - 121}}{4} \cr & = \frac{{ - 49}}{4} \cr & = - \frac{{49}}{4} \cr} $$