Quadratic Formula & Discriminants
CONCEPTS
Quadratic Formula
• x₁, x₂ = (–b ± √ (b² – 4ac)) / 2a
• Use the Quadratic formula when it's difficult to factor equation
Discriminant
• The discriminant is the equation, b² – 4ac (this is taken from the formula under the square root in the quadratic formula)
• If b² – 4ac > 0, there are 2 real solutions.
• If b² – 4ac = 0, there is 1 real solution.
• If b² – 4ac < 0, there are no real solutions.
PRACTICE PROBLEMS
Question 1 What are the solutions to x² - 5x + 3 = 0?
-- Answer -- (5 ± √13) / 2
x² – 5x + 3 = 0, use the quadratic formula
x₁, x₂ = (–b ± √ (b² – 4ac)) / 2a = (– (–5) ± √((–5)² – 4 * 1 * 3)) / (2 * 1) = (5 ± √(25 –12)) / 2 = (5 ± √13) / 2
Question 2 Does the quadratic formula 5x² + 10x + 9 = 0 have 2, 1, or 0 real solutions?
-- Answer -- 0
b² – 4ac = 10² – 4 * 5 * 9 = 100 – 180 = -80 => 0 real solutions
ACT PRACTICE PROBLEMS
