Minimum value of (x – 2) (x – 3) is:

Formula:

When a > 0 (In the equation ax² + bx + c), then

The minimum value of the equation is = (4ac – b²)/4a

Calculation:

(x – 2) (x – 3)

⇒ x² – 2x – 3x + 6

⇒ x² – 5x + 6

Comparing ax² + bx + c = 0

a = 1, b = -5 and c = 6

⇒ a = 1 (a > 0)

Then, minimum value = (4 × 1 × 6 – (-5²)/4

∴ Minimum value = (24 – 25)/4 = -1/4

2nd approach (Differentiation method)

(x – 2) (x – 3)

⇒ x2 – 5x + 6

Differentiating, we get

2x - 5 = 0

⇒ x = 5/2

Hence, minimum value = (5/2 – 2) (5/2 – 3) = 1/2 × - (1/2) = -1/4