Q1 of 55 Page 1

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

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.


 

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