Multiply using the distributive property

What you'll learn

• Identify the number of real roots of a quadratic equation (ax² + bx + c = 0) by calculating the discriminant (b² - 4ac) and relating its value to the nature of the roots (two distinct real roots, one real root, or no real roots) with 80% accuracy.
• Solve for the discriminant (b² - 4ac) of a given quadratic equation (ax² + bx + c = 0) and correctly classify the roots as real and distinct, real and equal, or non-real with 90% accuracy.
• Explain how the discriminant (b² - 4ac) of a quadratic equation (ax² + bx + c = 0) can be used to determine the number and type of solutions to the equation, justifying the relationship between the discriminant's sign and the root's nature in a written explanation with at least 3 supporting statements.
• Apply the discriminant to determine the value(s) of a parameter (k) in a quadratic equation (ax² + bx + c = 0) such that the equation has a specified number of real roots (e.g., two distinct real roots, one real root, or no real roots), solving problems with 75% accuracy.