Algebra 2 Quiz Discriminant Flashcards

Discriminant in Quadratic Equations

• The discriminant is represented by the formula b² - 4ac in a quadratic equation.
• Indicates the nature of the roots of a quadratic equation.

Solutions Based on the Discriminant

• A negative discriminant indicates no real solutions exist.
• A zero discriminant signifies one real solution, known as a repeated root.
• A positive discriminant means there are two distinct real solutions.

Quadratic Equation Characteristics

• Quadratic equations are also referred to as second-degree equations.
• The standard form of a quadratic equation is expressed as ax² + bx + c = 0.

True or False Statements

• It is false that quadratic equations always have two real solutions.
• It is true that all real numbers qualify as complex numbers.

Roots and Solutions

• A quadratic equation may have a repeated root, also referred to as a root of multiplicity two.
• An extraneous solution arises when a solution does not satisfy the original equation.

Complex Numbers

• In the complex number 5 + 2i, the number 5 is termed the real part.
• The number 2 is the imaginary part, while i denotes the imaginary unit.

Example and Conjugates

• For the equation x² = -4, the solution set is {-2i, 2i}.
• The conjugate of a complex number, such as 2 + 5i, is obtained by changing the sign of the imaginary part, resulting in 2 - 5i.

Radical Equations

• Radical equations can occasionally yield no real solutions, making it essential to check for extraneous solutions.

Textbook References

• Specific tasks such as checking items on designated pages (e.g., #8 on page 127, #7 on page 134) are recommended for detailed understanding.