📖Definition
The quadratic formula is a mathematical formula that provides the solution(s) to a quadratic equation of the form ax² + bx + c = 0. It gives you the values of x that make the equation true.
📐Formula
In this formula: a is the coefficient of x², b is the coefficient of x, c is the constant term, and the ± symbol means you calculate two solutions (one with + and one with -).
📝Step-by-Step Guide
Identify the coefficients
Write your equation in standard form (ax² + bx + c = 0) and identify the values of a, b, and c.
Calculate the discriminant
The discriminant tells you how many solutions exist. Calculate b² - 4ac.
Apply the formula
Substitute your values into the quadratic formula and simplify.
Calculate both solutions
Use the + sign for one solution and the - sign for the other.
⚠️Common Mistakes to Avoid
- Forgetting to include the negative sign in front of b
- Making errors when calculating the discriminant (b² - 4ac)
- Dividing only part of the numerator by 2a instead of the entire expression
- Not simplifying the square root when possible
- Forgetting that ± gives two different answers
✏️Practice Problems
Solve x² - 5x + 6 = 0
💡 Hint: Identify a=1, b=-5, c=6
Answer: x = 2 or x = 3
Solve 2x² + 7x - 15 = 0
💡 Hint: Remember to use a=2 when dividing
Answer: x = 1.5 or x = -5
Solve 3x² - 2x - 8 = 0
Answer: x = 2 or x = -4/3
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