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Quadratic Equation by Formula

The general quadratic equation is

Multiplying by 4a we get 4a²x² + 4abx + 4ac = 0

The two roots of the above quadratic equation are

Nature of roots :

(i) If the roots are real and unequal.

(a) If and perfect square, the roots are rational provided a, b, c are rational
(b) If and not perfect square, the roots and are irrational

(ii) If D = 0, roots are real and equal

(iii) If D < 0, roots are imaginary.