The discriminant gives the type of solutions that will be found for a
quadratic equation.
The number of real solutions for the quadratic formula is one.
Reasons:
If the discriminant in the quadratic formula, y = a·x² + b·x + c, is the value;
\(\mathbf{b^{2}-4\cdot a\cdot c}}\ \ in \ x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}\)
Where;
a, b, and c are real numbers, we have
A zero discriminant gives;
\(x = \dfrac{-b\pm \sqrt{0}}{2\cdot a} = \dfrac{-b\pm0}{2\cdot a} = \dfrac{-b}{2\cdot a}\)
Therefore;
\(x = \dfrac{-b}{2\cdot a}\)
\(\dfrac{-b}{2\cdot a}\) is one real number
Therefore;
The number of real solutions for the quadratic formula is one.
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