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2014-07-01T16:33:18+08:00

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The nature of the roots may be determined by solving for the value of the discriminant.

discriminant = positive   :     2 distinct real roots
                   = 0             :     2 equal real roots
                   = negative   :     2 distinct unreal roots


given ax² +bx +c = 0

discriminant = b² -4ac


For x²+6x+3=0,

discriminant = 6
² - 4(1)(3)
                   = 36 -12
                   = 28

The discriminant of x²+6x+3=0 is positive, therefore it has 2 distinct real roots.
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