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,

the answer to this question is 3/19

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204