Solving Quadratic Equations with Complex Roots

What is the quadratic formula used for?

• To find the solutions or roots of a quadratic equation.

• To find the sum of two numbers.

• To calculate the area of a triangle.

• To determine the slope of a line.

Answer explanation

The quadratic formula is used to find the solutions or roots of a quadratic equation.

When does a quadratic equation have complex solutions?

• When the discriminant is positive.

• When the quadratic equation has only one solution.

• When the discriminant is zero.

• When the discriminant is negative.

Answer explanation

A quadratic equation has complex solutions when the discriminant is negative.

Avery, Ethan, and Rohan are having a heated debate about quadratic equations. They are trying to figure out the difference between real and complex solutions. Can you help them out?

• Real solutions are complex numbers, while complex solutions involve real numbers.

• Real solutions are rational numbers, while complex solutions involve irrational numbers.

• Real solutions are real numbers, while complex solutions involve imaginary numbers.

• Real solutions are positive numbers, while complex solutions involve negative numbers.

Answer explanation

Real solutions are real numbers, while complex solutions involve imaginary numbers.

If the discriminant is negative, then the quadratic has:

• 1 Real Solution

• 2 Real Solutions

• Half a Solution

• 2 Complex (imaginary) Solutions

The discriminant is

• aX²  + bX  +  c

• b - 4ac

• b² - 4ac

• b² + 4ac

Determine the value of the discriminant and describe the number and type roots for the following:

x² + 7x + 13

• 101, 2 real roots

• 3, 2 real roots

• -101, 2 imaginary roots

• -3, 2 imaginary roots

What is this formula?

• This is the speed of light formula.

• This is the quadratic formula.

• This is the zero product property.

• This is scary.

Solve using the quadratic formula. f(x) = 2x²- 4x + 7

• (2±2i√10)/2

• (4±√40)/4

• (2±i√10)√/2

• (2±2i√40)/4

The discriminant is

• ax² + bx + c

• b - 4ac

• b² - 4ac

• b² + 4ac