A quadratic equation in x is an equation that can be written in the standard from ax2 + bx +c = 0
where a, b, and c are real numbers with a ≠ 0. A quadratic equation in x is also called a second-degree polynomial equation in x
The Zero-Product Principle
If the product of two algebraic expressions is zero, then at least one of the factors is equal to zero.
.If AB = 0, then A = 0 or B = 0.
Solving a Quadratic Equation by Factoring
3. Apply the zero-product principle, setting each factor equal to zero.
4. Solve the equations in step 3.
5. Check the solutions in the original equation.
Ex 1 Solve by factoring:
Solution set is
1. Solution set
The Square Root Method
Ex 2 Solve by the square root method:
Completing the Square
If x2 + bx is a binomial, then by adding , which is the square of half the coefficient of x, a perfect square trinomial will result..
Ex 3 What term should be added to the binomial
so that it becomes a perfect square trinomial?
Add the constant
Factor the trinomial
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial.
Then factor the trinomial