G. The Discriminant
Completion requirements
G. The Discriminant
Not all quadratic equations will have two unique and Real solutions. If the radicand in the quadratic formula is zero, there will be two equal solutions. If the radicand is negative, there will be no Real solutions because the square root of a negative number is a complex number. Because the radicand has such a determining effect, it is called the discriminant. By finding just the
discriminant,
you can determine whether the quadratic equation has zero, one, or two Real solutions, which is the nature of the roots.
Quadratic Formula
Discriminant
\(b^2 - 4ac\)
The Discriminant
Quadratic Formula
\[x = \frac{{ -b \pm \sqrt {{\color{red}b^2 - 4ac}} }}{{2a}}\]
Discriminant
\(b^2 - 4ac\)
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The Discriminant
The discriminant tells about the nature of the roots of a
quadratic equation
.
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If \(b^2 - 4ac < 0\), there are zero Real roots.
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Note: The graph of the related quadratic function has no \(x\)-intercepts. |
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If \(b^2 - 4ac = 0\), there are two equal, Real roots.
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Note: The graph of the related quadratic function has one \(x\)-intercept. |
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If \(b^2 - 4ac > 0\), there are two distinct, Real roots.
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Note: The graph of the related quadratic function has two \(x\)-intercepts. |