{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mac1140_lecture8_2 - L8 2.4 Quadratic Equations Example...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
62 L8 §2.4 Quadratic Equations The quadratic equation is an equation that can be written in the form 2 0 ax bx c + + = where a, b, and c are real numbers and 0 a . Solving by factoring Zero-Factor Property : If 0 ab = , then 0 a = , or 0 b = , or both. This property can be applied to more than two factors. Important: Always set an equation of degree 2 or higher equal to zero before applying the Zero-Factor property . Example : Solve 2 3 18 21 x x + = . 63 Example : Solve 3 4 x x = . Square Root Property : The solution set to 2 x k = is x k = ± . Note : If 0 k , k is the principle square root (nonnegative). If 0 k < , k i k = (imaginary number). Example . Solve each quadratic equation: a) 2 32 x = − b) 2 ( 3) 49 z =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
64 Completing the Square : We can solve a quadratic equation 2 0 ( 0) ax bx c a + + = by completing the square . Steps (must be memorized) : 1. Make sure that 1 a = ; if not, divide each term by a . 2. Get the constant on the right side of the equation. 3. Take 1/2 of the coefficient of x and square it. 4. Add this number to both sides of the equation. 5. Factor the left-hand side into a perfect square. 6. Solve for
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}