University:
High School
Course:
High School Algebra
Academic year:

2021
Views:

426

Pages:

6
Author:

Saniyah Lambert

To find the solutions to a quadratic equation, factor the equation, then use the Zero Product Property to find the roots. Zero Product Property If the product of two quantities equals zero, then at least one of the quantities equals zero. If a(b) = 0, then a = 0 or b = 0 Example: Find the roots of 2x² - 8x 2x(x - 4) = 0 (Factor) 2x = 0 or x - 4 = 0 (Set the equation equal to zero) 2x/2 = 0/2 or x = 4 (Use the Zero Product Property to solve for x) x = 0 or x = 4 (The solutions are called the roots and are the x-intercepts of the equation.) Examples: Find the solutions to the quadratic equations. 4g² - 40g y² - 4y - 12 x² - 9 You Try! 4x² - 9 5z² + 45z n² - 10n + 9 To find the solutions to a quadratic equation, factor the equation, then use the Zero Product Property to find the roots. Zero Product Property If the product of two quantities equals zero, then at least one of the quantities equals zero. If a(b) = 0, then a = 0 or b = 0 Example: Find the roots of 2x² - 8x 2x(x - 4) = 0 (Factor) 2x = 0 or x - 4 = 0 (Set the equation equal to zero) 2x/2 = 0/2 or x = 4 (Use the Zero Product Property to solve for x) x = 0 or x = 4 (The solutions are called the roots and are the x-intercepts of the equation.) Examples: Find the solutions to the quadratic equations. 4g² - 40g = 0 4g(g - 10) = 0 4g = 0 or g - 10 = 0 g = 0 or g = 10 y² - 4y - 12 = 0 (y - 6)(y + 2) = 0 y - 6 = 0 or y + 2 = 0 y = 6 or y = -2 x² - 9 = 0 (x + 3)(x - 3) = 0 x + 3 = 0 or x - 3 = 0 x = -3 or x = 3 You Try! 4x² - 9 = 0 (2x + 3)(2x - 3) = 0 2x + 3 = 0 or 2x - 3 = 0 x = -3/2 or x = 3/2 5z² + 45z = 0 5z(z + 9) = 0 5z = 0 or z + 9 = 0 z = 0 or z = -9 n² - 10n + 9 = 0 (n - 9)(n - 1) = 0 n - 9 = 0 or n - 1 = 0 n = 9 or n = 1 Simplifying Square Roots: Factor the radicand to its prime factors. (Hint: use a factor tree.) Every group of 2 factors is replaced by one factor outside of the radical. Extra factors are left inside the radical. Multiply all outside numbers together. Multiply all remaining factors inside the radical together.1 Example: √96 = √2 * 2 * 2 * 2 * 3 = √(2 * 2) * (2 * 2) * 3 = 2 * 2√3 = 4√6 Examples: Ex 1: √75 Ex 2: 3√54 Ex 3: √24x⁵ You Try: √24 3√49x²