<PRE><B>Question 59581</B>
1. 2x^2 + x - 1 = 0

Here a = 2,  b = 1  and c = -1

Discriminant D = b^2 - 4ac
               = 1^2 - 4(2)(-1)
               = 1 +8
               = 9

9 is positive and a perfect square.
So the two roots of the given equation are real and rational.


b)  4/3 x^2 -2x + 3/4 = 0

Here a = 4/3,  b= -2  and c= 3/4

Discriminant = D = b^2 - 4ac
                 = (-2)^2 - 4(4/3)(3/4)

                 = 4 - 4
                 = 0

As the discriminant is zero, the given equation has two real and equal roots.

c) m^2 + m + 1 = 0

Here a = 1,  b = 1  and c = 1.

Discriminant = D = b^2 - 4ac
                 = 1^2 - 4(1)(1)
                 = 1 - 4
                 = -3

D is negative and so both the roots of the given equation are complex.

Good Luck!!!





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