Operations with imaginary numbers and Quadratic Formula

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 imaginary 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 √-1?

Back

√-1 = i.

Front

What is the result of √-81?

Back

√-81 = 9i.

Front

How do you simplify the expression 2i - 7i + 10?

Back

2i - 7i + 10 = 10 - 5i.

Front

What is the product of (-3i)(4i)(-5i)?

Back

(-3i)(4i)(-5i) = -60i.

Front

What is the discriminant in the quadratic formula?

Back

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

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that there are two distinct real solutions.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that there is exactly one real solution (a repeated root).