ind the roots of the equation x2 – 3x – m (m + 3) = 0

Sure, let's solve the equation step by step.

The given equation is a quadratic equation of the form ax^2 + bx + c = 0, where a = 1, b = -3, and c = -m(m+3).

The roots of a quadratic equation can be found using the formula:

x = [-b ± sqrt(b^2 - 4ac)] / (2a)

Here, b^2 - 4ac is called the discriminant. The nature of the roots depends on the discriminant.

Let's calculate the discriminant:

D = b^2 - 4ac = (-3)^2 - 41(-m(m+3)) = 9 + 4m^2 + 12m = 4m^2 + 12m + 9

The roots of the equation are real and distinct if D > 0, real and equal if D = 0, and complex if D < 0.

So, the roots of the equation x^2 – 3x – m(m + 3) = 0 are:

x = [3 ± sqrt(4m^2 + 12m + 9)] / 2

This is the general solution. The exact roots will depend on the value of m.