Roots of the Equation x²-3x-m(m+3)=0
The given equation is x²-3x-m(m+3)=0 where m is a constant. We need to find the roots of this equation in terms of m.

Finding the Roots
To find the roots of the equation x²-3x-m(m+3)=0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax²+bx+c=0, the roots are given by x = (-b ± √(b²-4ac)) / 2a.
In this case, the coefficients of the equation x²-3x-m(m+3)=0 are a=1, b=-3, and c=-m(m+3). Substituting these values into the quadratic formula, we get x = (3 ± √(9+4m(m+3))) / 2.

Simplifying the Roots
To simplify the roots further, we need to simplify the expression under the square root. This gives us x = (3 ± √(9+4m²+12m)) / 2. Simplifying the expression further, we get x = (3 ± √(4m²+12m+9)) / 2.
Now, we can further simplify the expression under the square root to get x = (3 ± (2m+3)) / 2. This gives us the roots of the equation x²-3x-m(m+3)=0 in terms of the constant m.
Therefore, the roots of the equation x²-3x-m(m+3)=0 are x = (3 + 2m + 3) / 2 and x = (3 - 2m - 3) / 2, which simplifies to x = 2m + 3 and x = -m.