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Solving a Quadratic Equation

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Quadratic Equations

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
1. If necessary, rewrite the equation in the form ax² + bx +c = 0, moving all terms to one side, thereby obtaining zero on the other side.

2.Factor.

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

Continued

Solution set is

Practice Exercises

Solve:

Answers

1. Solution set

2.Solution set

The Square Root Method

If x² = p and p ≥ 0, then

Equivalently,

If x² = p then .

Ex 2 Solve by the square root method:

Solution

Solution set:

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

Practice Exercise

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial.

Then factor the trinomial

Answer