The roots of the equation x² - 3x-m(m+3)= 0, where m is constant, are a. m, m+3 c. m +3,-m b. m, -(m+3) d. (m+3), -m

The roots of a quadratic equation are given by the formula:

x = [ -b ± sqrt(b² - 4ac) ] / 2a

In the given equation x² - 3x - m(m+3) = 0, we can identify a, b, and c from the standard form of a quadratic equation ax² + bx + c = 0. Here, a = 1, b = -3, and c = -m(m+3).

Substituting these values into the quadratic formula gives:

x = [ 3 ± sqrt((-3)² - 41-m(m+3)) ] / 2*1 x = [ 3 ± sqrt(9 + 4m² + 12m) ] / 2 x = [ 3 ± sqrt(4m² + 12m + 9) ] / 2 x = [ 3 ± sqrt((2m + 3)²) ] / 2 x = [ 3 ± (2m + 3) ] / 2

This simplifies to two possible solutions for x:

x = (3 + 2m + 3) / 2 = m + 3 x = (3 - 2m - 3) / 2 = -m

So, the roots of the equation are m + 3 and -m. Therefore, the correct answer is (d) (m+3), -m.