Question

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

Options

• 0

• 4

• 6

• none of these

Answer 1

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

Explanation:

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