Question

If the quadratic equation, `px^2 - 2sqrt(5)px + 15 = 0` has two equal roots, then the value of p is ______.

Options

• 0

• 3

• 6

• both 0 and 3

Answer 1

If the quadratic equation, `px^2 - 2sqrt(5)px + 15 = 0` has two equal roots, then the value of p is 3.

Explanation:

Comparing `px^2 - 2sqrt(5)px + 15 = 0` with ax² + bx + c = 0 we get,

a = p, b = `-2sqrt(5)p` and c = 15.

We know that,

Since equations has equal roots,

⇒ D = 0

⇒ b² – 4ac = 0

⇒ `(-2sqrt(5)p)^2 - 4(p)(15) = 0`

⇒ 20p² – 60p = 0

⇒ 20p(p – 3) = 0

⇒ 20p = 0 or (p – 3) = 0   ...[Using zero-product rule]

⇒ p = 0 or p = 3

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

p = 3