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