Quadratic Formula and Complex Numbers

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does i represent in complex numbers?

Back

i represents the imaginary unit, defined as the square root of -1.

Front

What is the value of i²?

Back

i² = -1.

Front

How do you simplify the expression -3i(4 + 2i)?

Back

The simplified form is 6 - 12i.

Front

What are the coefficients a, b, and c in the quadratic equation 4x² - 8x = 3?

Back

a = 4, b = -8, c = -3.

Front

How do you simplify the expression (2 - 3i)(5 + 4i)?

Back

The simplified form is 22 - 7i.

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

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.

Front

How do you add complex numbers (3 + 2i) + (4i + 6)?

Back

The sum is 9 + 6i.

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.