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Question

How many roots does the polynomial 3x2+3x+3=0 have?


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Solution

Finding the root of the equation:

We know for the quadratic equation ax2+bx+c=0 if

  1. b2-4ac>0 then there are two roots the roots are real
  2. b2-4ac=0 then roots are real and of order two
  3. b2-4ac<0 then there are two roots the roots are complex root

Given quadratic equation is 3x2+3x+3=0

Now comparing with the standard form we have a=3,b=3,c=3.

b2-4ac=32-4·3·3=9-36=-27b2-4ac<0

Since the value of (b2-4ac) is negative, 3x2+3x+3=0 has 2 complex roots which are complex conjugates of each other.

Hence the polynomial 3x2+3x+3=0 has 2 complex roots.


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