Thus, the quadratic equation has two real and different roots when b 2 - 4ac > 0. Nature of Roots When D > 0Īnd it gives us two real and different roots. Since the discriminant D is in the square root, we can determine the nature of the roots depending on whether D is positive, negative, or zero. So this can be written as x = (-b ± √ D )/2a. The quadratic formula is x = (-b ± √ (b 2 - 4ac) )/2a. The discriminant of the quadratic equation ax 2 + bx + c = 0 is D = b 2 - 4ac. We can determine the nature of the roots by using the discriminant. But for finding the nature of the roots, we don't actually need to solve the equation. and so we can say that the equation has two real and different roots.
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