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| Nature of the roots |
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| Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. |
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| i) D>0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). |
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| ii) D>0 i.e., perfect square. The roots are rational and distinct. |
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| iv) D < 0 i.e., negative. The roots are complex and always occur in conjugate pairs. |
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