If the roots of the quadratic equation, px(x - 2) + 6 = 0 are equal, then the value of p is:

1. 0

2. 4

3. 6

4. none of these

Given,

⇒ px(x - 2) + 6 = 0

⇒ px² - 2px + 6 = 0

Comparing px² - 2px + 6 = 0 with ax² + bx + c = 0 we get,

a = p, b = -2p and c = 6.

We know that,

Since equations has equal roots,

⇒ D = 0

⇒ b² - 4ac = 0

⇒ (-2p)² - 4(p)(6) = 0

⇒ 4p² - 24p = 0

⇒ 4p(p - 6) = 0

⇒ 4p = 0 or p - 6 = 0      [Using Zero-product rule]

⇒ p = 0 or p = 6.

Since p = 0 would make the equation no longer quadratic, we take:

p = 6

Hence, option 3 is the correct option.