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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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