The discriminant is the name given to the expression that appears under
the square root (radical) sign in the quadratic formula.
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Quadratic Formula:
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Discriminant
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The discriminant tells you about the "nature" of the roots
of a quadratic equation given that a, b and c are rational numbers.
It quickly tells you the number of real roots, or in other words, the
number of x-intercepts, associated with a quadratic equation.
There are three situations:
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Value of the discriminant |
Example showing nature of roots of ax2
+ bx + c = 0 |
Graph indicating x-intercepts
y = ax2 +
bx + c |
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POSITIVE
 |
There
are two real roots.
(If the discriminant is a perfect
square, the two roots are rational numbers. If the
discriminant is not a perfect square, the two roots are
irrational numbers containing a radical.) |
There are two x-intercepts. |
|
ZERO |
There is one real root.
(The root is repeated.)
|
There is one x-intercept.
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NEGATIVE |
There
are two complex roots.
|
There are no x-intercepts. |
