*Quadratics and Complex Numbers Review

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you add two polynomials?

Back

To add two polynomials, combine like terms by adding their coefficients.

Front

What is the product of two complex numbers (a + bi)(c + di)?

Back

The product is (ac - bd) + (ad + bc)i.

Front

What is the result of multiplying (5 - 3i)(5 + 3i)?

Back

The result is 34.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to ac and add to b, then rewrite the expression.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is b² - 4ac and determines the nature of the roots.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex.

Front

How do you divide a polynomial by a binomial?

Back

Use polynomial long division or synthetic division.