Find the roots of the equation x² - 3x- m (m + 3) = 0, where m is a constant. (CBSE 2011)

Here, on comparing with general equation ax ² + bx + c = 0, we get

a = 1

b = - 3

c = - m(m + 3)

Now, Discriminant = D = (b² – 4ac)

∴ D = [9 -4 × (-m(m + 3))]

= [9 + 4m² + 12 m]

= (2m + 3)²

Therefore roots of the equation are given by:

x = (-b ± √D)/2a

∴ x = (3 ± (2m + 3))/2

= [(6 + 2m)/2] or [-2m/2]

= 3 + m or – m.

Thus the roots of the equation are: - m and m + 3.