The Quadratic Formula
The quadratic formula x = (-b ± √(b²-4ac)) / 2a solves any quadratic equation ax² + bx + c = 0, including those that cannot be factorised.
What You Need to Know
Key Concept Diagram
The quadratic formula is x = (-b ± √(b²-4ac)) / 2a for ax² + bx + c = 0
The discriminant Δ = b²-4ac determines the number of solutions: positive → 2, zero → 1, negative → 0
Always rearrange to standard form ax² + bx + c = 0 before identifying a, b, c
Leave answers in exact surd form unless a decimal is requested
Key Vocabulary
Quadratic formula
The formula x = (-b ± √(b²-4ac)) / 2a used to solve any quadratic equation
Discriminant
The expression b²-4ac that tells how many real solutions exist
Surd
An exact irrational expression containing a square root
Standard form
A quadratic written as ax² + bx + c = 0 with the right-hand side equal to zero
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Use the quadratic formula to solve x² + 5x + 6 = 0. Which values of a, b, c are correct?
Question 2
For x² - 4x + 4 = 0, what is the discriminant?
Question 3
How many real solutions does x² + x + 5 = 0 have?
Key Concepts Summary
- ●The quadratic formula is x = (-b ± √(b²-4ac)) / 2a for ax² + bx + c = 0
- ●The discriminant Δ = b²-4ac determines the number of solutions: positive → 2, zero → 1, negative → 0
- ●Always rearrange to standard form ax² + bx + c = 0 before identifying a, b, c
- ●Leave answers in exact surd form unless a decimal is requested