Unformatted text preview: Solving Quadratic
Solving
Equations Algebraically
Equations
Section 2.2 Defn. of Quadratic Equation
Defn. A quadratic or second degree, equation is one that can be written in the form: ax + bx + c = 0, a ≠ 0
2 The Zero Product Property
The If a product of real numbers is zero, then at least one of the factors is zero.
If ab = 0, then a = 0 or b = 0 (or both) Completing the Square
Completing
To complete the square of the expression x 2 + bx , add the square of onehalf the coefficient of x, namely . b 2 ÷
2 The addition produces a perfect square trinomial. 2 2 b
b x + bx + ÷ = x + ÷
2
2 2 Solve by completing the square. 2x − 6x +1 = 0
2 2 x − 6 x = −1 subtract 1
1
2
x + 3 x + ___ = − + ___
2 Divide by 2
2 9
19
x − 3x + = − + Add half of 3 squared
4
24
2 2 3 7 Rewrite as perfect x− ÷ =
2
4 square and simplify
3
7
x− =±
2
2 The Quadratic Formula
The The solutions of the quadratic equation 2 are
ax + bx + c = 0 −b ± b − 4ac
x=
2a
2 The Discriminant
The
Discriminant Value Number of Real Solutions b − 4ac > 0 2 distinct real solutions b − 4ac = 0 1 distinct real solution 2 2 b − 4ac < 0
2 0 real solutions Joke Time
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 Winter '11
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 Calculus, Algebra, Equations, Quadratic equation, Elementary algebra, real solutions, ax + bx, perfect square trinomial.

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