Given the quadratic equation: x^2 + px + (1-p) = 0, we are asked to find the roots of this equation when (1-p) is a root.



To find the roots of the quadratic equation, let's first write it in the standard form: ax^2 + bx + c = 0. Comparing this with the given equation, we can identify the values of a, b, and c as follows:

• a = 1


• b = p


• c = (1-p)

Now, let's use the quadratic formula to find the roots of the equation:

Quadratic Formula:
The roots of a quadratic equation in the standard form ax^2 + bx + c = 0 can be found using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c from our equation into the quadratic formula, we get:

x = (-(p) ± √((p)^2 - 4(1)(1-p))) / (2(1))

Simplifying further:

x = (-p ± √(p^2 - 4 + 4p)) / 2

x = (-p ± √(p^2 + 4p - 4)) / 2

Now, let's simplify the expression under the square root:

p^2 + 4p - 4 = (p^2 + 4p + 4) - 8 = (p + 2)^2 - 8

Therefore, the roots of the given quadratic equation are:

x = (-p ± √((p + 2)^2 - 8)) / 2



The roots of the quadratic equation x^2 + px + (1-p) = 0, when (1-p) is a root, are given by the expression x = (-p ± √((p + 2)^2 - 8)) / 2.