Quadratic Formula Discriminant and Complex Numbers

Use the graph to determine what type & numbers of solutions are shown.

• Two Real Solutions

• One Real Solution

• Two Non-Real Complex Solutions

• None of these Above

Determine the value of the discriminant and the number and the type of the solutions for the equation: x² + 2x - 63 = 0

• 256 , Two real solutions

• • - 256 , Two imaginary solutions

• • - 128 , Two imaginary solutions

For the function above, is the discriminant positive, negative, or zero?

• Positive

• Negative

• Zero

Use the quadratic formula to find the solutions of the equation

0 = x² - 5x - 12

• No Real Solution

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Mia, Sophia, and Ethan are in a heated debate about quadratic equations. They are trying to figure out what the discriminant of a quadratic equation is. Can you help them?

• Mia thinks the discriminant of a quadratic equation is always equal to zero.

• Sophia argues that the discriminant of a quadratic equation is the expression b² - 4ac.

• Ethan believes that the discriminant of a quadratic equation is the product of the coefficients a, b, and c.

• Or is it that the discriminant of a quadratic equation is the sum of the coefficients a, b, and c?

Answer explanation

The discriminant of a quadratic equation is the expression b^2 - 4ac, which determines the nature of the roots. It helps identify if the roots are real, imaginary, or equal.

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.

What is the role of the discriminant in a quadratic equation?

• The discriminant determines the nature of the roots of the quadratic equation.

• The discriminant is used to find the coefficient of the quadratic equation.

• The discriminant is used to simplify the quadratic equation.

• The discriminant is used to find the degree of the quadratic equation.

Answer explanation

The discriminant determines the nature of the roots of the quadratic equation.

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.

Which of the following indicates that a quadratic equation has complex solutions?

• The discriminant is greater than zero

• The discriminant is equal to zero

• The coefficients are all positive

• The discriminant is less than zero