mac1147_lecture5_1_b

mac1147_lecture5_1_b - L5 Quadratic Equations and the...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
50 L5 Quadratic Equations and the Quadratic Formula; Applications; Complex Numbers Quadratic Equations A quadratic equation is an equation of the form 2 0 ax bx c + += where a, b, and c are real numbers and 0 a . Solving by Factoring Zero-Product Property : If 0 ab = , then Example : Solve by factoring. 2 10 9 x x −= 2 41 2 9 0 x x −+ =
Background image of page 1

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

View Full DocumentRight Arrow Icon
51 The Square Roots Method : The solution set to 2 x p = (0 ) p is the set of all square roots of the number p , that is x p Example . Solve using the Square Roots Method. 2 25 x = 2 (2 )3 x += Solving Quadratic Equations by Completing the Square : 2 0, 0 ax bx c a + 1. Make sure that 1 a = ; if not, divide each term by a . 2. Get the constant on the right-hand side of the equation. 3. Take 1/2 of the coefficient of x , square it, and add this number to both sides of the equation. 4. Factor the left-hand side into a perfect square. 5. Solve for x using the Square Roots Method.
Background image of page 2
52 Example : Solve by completing the square. 2 83 0 x x −+ =
Background image of page 3

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

View Full DocumentRight Arrow Icon
53 The Quadratic Formula The quadratic equation 2 00 ax bx c a + += has the solutions 2 4 2 bb a c x a −± = The quantity 2 4 ba c , denoted D , is called the discriminant .
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 15

mac1147_lecture5_1_b - L5 Quadratic Equations and the...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online