Nature of the roots

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Without solving the quadratic equation, the nature of the roots can be determined using the discriminant.

i) D>0 i.e., positive and not a perfect square. The roots are real and distinct (irrational).

ii) D>0 i.e., perfect square. The roots are rational and distinct.

iv) D < 0 i.e., negative. The roots are complex and always occur in conjugate pairs.


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