When does a quadratic equation have only one root?  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A quadratic equation does not have one root, instead it is referred to as the equation having 2 equal roots.

A quadratic equation in the general form ax^2 + bx + c = 0 has the roots given by:

  • x1 = -b/2a + sqrt (b^2 – 4ac) / 2a
  • x2 = -b/2a – sqrt (b^2 – 4ac) / 2a

We see that the term differing in the two formulae is sqrt(b^2 – 4ac)

If b^2 – 4ac is equal to zero a quadratic equation will have equal roots.

The quadratic equation ax^2 + bx+ c = 0 has equal roots when b^2 = 4ac