Find the values of P for which the equation below has equal roots x^2 - (p-2)x + 2p + 1 = 0

p = 0, p = 12

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 then the nature of its roots is given by the discriminant

Δ = b² - 4ac

For equal roots b² - 4ac = 0

Given

x² -(p - 2)x + 2p + 1 = 0 ← in standard form

with a = 1, b = - (p - 2), c = 2p + 1, then

[- (p - 2)]² - (4 × 1 × 2p + 1) = 0

(p - 2)² - 4(2p + 1) = 0

p² - 4p + 4 - 8p - 4 = 0

p² - 12p = 0 ← factor out p from each term

p(p - 12) = 0

Equate each factor to zero and solve for x

p = 0

p - 12 = 0 ⇒ p = 12

Step-by-step explanation:

Given the equation:

.

Comparing it with , we get:

Equal Roots mean Discriminant = 0

So,