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Quadratic Equation
ax2 + bx + c = 0
Quadratic Equation Discriminant
b2 - 4ac
Quadratic Equation Discriminant In Use
b2 - 4ac > 0 => 2 different real roots
b2 - 4ac = 0 => 1 real root
b2 - 4ac < 0 => 0 real roots
Example 1
2x2 + 5x + 1 = 0
Using b2 - 4ac = 0 with
a = (2) b = (5) c = (1)
(5)2 - 4(2)(1) = 25 - 8 = 17
17 > 0 => 2 different real roots
Example 2
x2 - 4x + 4 = 0
Using b2 - 4ac = 0 with
a = (1) b = (-4) c = (4)
(-4)2 - 4(1)(4) = 16 - 16 = 0
0 = 0 => 1 real root
Example 3
3x2 + x + 1 = 0
Using b2 - 4ac = 0 with
a = (3) b = (1) c = (1)
(1)2 - 4(3)(1) = 1 - 12 = -11
-11 < 0 => 0 real roots
Diagrams + Questions With Revealable Answers
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