1. Quadratic Formula
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IDAHO
b2
−4ac = 0
5x2
+6x +1= 0
−6± 62
−4⋅5⋅1
2⋅5
=
−6±4
10
=x
=x − .2,−1{ }
x
Plug into
Quadratic
Formula
Simplify
Solve plus
and minus for
both solutions
-1.0 -0.5-1.5 0.5
-0.5
0.5
x =
−b ± b2
−4ac
2a
If
then
Quadratic
Formula
= ax2
+bx +c0
Discriminent
b2
−4ac < 0
b2
−4ac > 0Two real solutions when
One real solution when
Zero real solutions and
Two complex solutions
when
Rule
Example 2Example 1
Two real solutionsZero real solutions and
Two complex solutions
x2
−4x +5= 0
x =
4± 42
−4⋅1⋅5
2⋅1
x =
4± −4
2
x =
4±2i
2
x = 2+i , 2−i{ }
2.0
0.5
1.0
1.5
0.5 1.0 1.5 2.0 2.5 3.0
the two complex
solutions
no real solutions because
function does not cross x-axis