Quadratic Equations: Nature of Roots
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 Quadratic Equations: Nature of Roots Example: Determine the nature of the roots of the followings quadratic equations: (i) x2 -5x + 3 = 0 Solution: (i) The given quadratic equation is:   x2 - 5x + 3 = 0 here a = 1, b = -5, and c = 3. D = b2 - 4ac = (-5)2 - 4 * 1 * 3 = 25 - 12 = 13 Since D > 0, therefore roots of the given equation are real and distinct.
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 (ii) 4x2 + 7x + 4 = 0 Solution: (ii) The given quadratic equation is: 4x2 + 7x + 4 = 0 here a = 4, b = 7, and c = 4. D = b2 - 4ac = (7)2 - 4 * 4 * 4 = 49 - 64 = -15 Since D < 0, therefore roots of the given equation are not real.

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