Quadratic_formula

State the Quadratic Formula

Hint: For ax² + bx + c = 0

What is the discriminant?

Hint: The expression under the square root in the quadratic formula

If the discriminant > 0, how many real solutions?

Hint: Positive discriminant means two distinct roots

If the discriminant = 0, how many real solutions?

Hint: Zero discriminant means the parabola touches the x-axis once

If the discriminant < 0, how many real solutions?

Hint: Negative discriminant means no real roots (complex roots)

Solve: x² - 5x + 6 = 0

Hint: Factor or use the quadratic formula with a=1, b=-5, c=6

Solve: x² + 4x + 4 = 0

Hint: Perfect square trinomial; discriminant = 0

Solve: x² - 4 = 0

Hint: Factor as difference of squares, or use quadratic formula

Solve: 2x² - 8 = 0

Hint: Divide by 2 first: x² = 4

Find the discriminant of x² + 3x + 5 = 0

Hint: b² - 4ac = 9 - 20 = -11 (no real solutions)