Question

Find the value of p for which the roots of the equation px (x − 2) + 6 = 0, are equal.

Answer 1

The given quadratic equation is px(x − 2) + 6 = 0.

Let us factorize the given quadratic equation.

px(x − 2) + 6 = 0

∴ px² − 2px + 6 = 0

Since the roots of the given quadratic equation are equal, its discriminant is equal to 0.

⇒ D = 0

⇒ b² − 4ac = 0

⇒ (− 2p)² − 4 × p × 6 = 0 [a = p, b = −2p, c = 6]

⇒ 4p² − 24p = 0

⇒ 4p (p − 6) = 0

⇒ 4p = 0 or p − 6 = 0

⇒ p = 0 or p = 6

Thus, the value of p is 0 or 6.