Solving Quadratic Equations: Methods and Examples
This page presents a comprehensive overview of solving quadratic equations through various methods, including factoring and the quadratic formula. The content is structured around three detailed examples that progressively increase in complexity.
Definition: Difference of squares is a binomial where both terms are perfect squares and are subtracted, following the pattern a² - b² = a+b$$a-b.
Highlight: The degree of an equation determines the number of solutions it will have.
Example One demonstrates solving x² = -4x:
Example: The solution process involves:
- Writing in standard form
- Factoring out GCF
- Setting factors equal to zero Solutions: x = 0 and x = -4
Example Two shows solving x² = -4x + 5:
Example: Key steps include:
- Standard form arrangement
- Discriminant checking
- Factoring Solutions: x = 1 and x = -5
Example Three tackles 3x² + 11x - 6:
Vocabulary: Discriminant - a value that helps determine the nature of solutions in a quadratic equation.
Highlight: The quadratic formula is essential when factoring isn't immediately obvious.