Solving Quadratics with Complex Solutions

Front

What is the general form of a quadratic equation?

Back

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

Front

What are complex solutions in the context of quadratic equations?

Back

Complex solutions are solutions to quadratic equations that include imaginary numbers, typically expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Tags

CCSS.HSN.CN.A.1

Front

How do you determine if a quadratic equation has complex solutions?

Back

A quadratic equation has complex solutions if the discriminant (b² - 4ac) is less than zero.

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant of a quadratic equation?

Back

The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula D = b² - 4ac. It determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, which allows for easier solving of the equation.

Tags

CCSS.HSA-REI.B.4B

Front

What are the steps to solve a quadratic equation using the quadratic formula?

Back

1. Identify coefficients a, b, and c. 2. Calculate the discriminant D = b² - 4ac. 3. Use the quadratic formula x = (-b ± √D) / (2a) to find the solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

How can you express complex solutions in terms of real and imaginary parts?

Back

Complex solutions can be expressed as a + bi, where a is the real part and b is the imaginary part.

Tags

CCSS.HSN.CN.A.1

Front

What is the significance of the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, and it is used to express complex numbers.

Tags

CCSS.HSN.CN.A.1

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the quadratic equation in the form (x - p)(x - q) = 0, then set each factor equal to zero to find the solutions.

Tags

CCSS.HSA-REI.B.4B