Quadratic Equations and Complex Numbers

These flashcards cover essential concepts related to quadratic equations and complex numbers based on the provided lecture notes.

What are the methods to solve quadratic equations?

Factoring, square root property, completing the square, and using the quadratic formula.

How can you add and subtract complex numbers?

Combine the real parts and the imaginary parts separately.

What is the definition of an imaginary number?

An imaginary number is defined as the square root of a negative number.

What is the standard form of a complex number?

A complex number is expressed in standard form as a + bi, where a is a real number and b is an imaginary number.

What does the discriminant of a quadratic equation tell us?

It tells how many solutions to expect for the quadratic equation.

How do you use the zero-product property in solving quadratics?

If the product of two expressions is zero, then at least one of the expressions must equal zero.

What is the formula to find the solutions of a quadratic equation using the quadratic formula?

x = (-b ± √(b² - 4ac)) / (2a)

In complex numbers, what does i represent?

i represents the imaginary unit, where i² = -1.

What is the process for solving polynomial equations by factoring?

Look for two numbers that multiply to ac (the product of a and c) and add to b, rewrite the quadratic, then factor it.

What indicates a rational exponent?

A rational exponent can be expressed as a fraction, showing the root and power.