Sheet № 204 · Higher only · AQA · Edexcel · OCR
Quadratic Formula and Discriminant –
The quadratic formula and discriminant are essential Higher tier GCSE Maths topics. The formula solves any quadratic equation, while the discriminant tells you how many real solutions to expect before you even start solving.
§Key definitions
Question:
This is a Higher only topic. Here is a straightforward example. Solve x² + 5x + 6 = 0 using the quadratic formula.
Answer:
x = -2 or x = -3
Q1 (Higher):
Calculate the discriminant of 3x² + 2x - 5 = 0 and state the number of solutions.
Q2 (Higher):
Solve x² - 6x + 2 = 0, giving answers to 2 decimal places.
Q3 (Higher):
The equation x² + px + 9 = 0 has no real solutions. Find the range of values of p.
§Formulas to memorise
x = (-b ± √(b² - 4ac)) / (2a)
Discriminant = b² - 4ac
If b² - 4ac = 0, there is one repeated real solution (the parabola just touches the x-axis).
Write the equation in the form ax² + bx + c = 0 and identify a, b, and c.
Worked example
This is a Higher only topic. Here is a straightforward example. Solve x² + 5x + 6 = 0 using the quadratic formula.
Working:
⚠ Common mistakes
- ✗Using the wrong sign for b. In the formula, the first term is -b. If b = -3, then -b = 3 (positive). Students often keep the negative sign, making -b = -3.
- ✗Forgetting to divide the entire numerator by 2a. The division applies to both -b and the ±√(b² - 4ac) part, not just the square root.
- ✗Not writing the equation as = 0 before identifying a, b, c. If the equation is x² + 3x = 7, you must rewrite as x² + 3x - 7 = 0 first.
✦ Exam tips
- →If the question asks for answers to a given number of decimal places, the quadratic formula is usually the intended method (not factorising).
- →Calculate the discriminant first and write it down — you earn a method mark even if you make an error in the final calculation.
- →When asked "how many solutions," you only need the discriminant — you do not need to solve the equation fully.