This study notes covers Worked Example 2: Surd Answer within Quadratic Formula for GCSE Mathematics. Revise Quadratic Formula in Algebra for GCSE Mathematics with 11 exam-style questions and 5 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 7 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 7
Practice
11 questions
Recall
5 flashcards
Worked Example 2: Surd Answer
Solve: x² + 4x - 1 = 0, giving answers in surd form
Step 1 Identify a, b, c
a = 1, b = 4, c = -1
Step 2 Calculate b² - 4ac
b² - 4ac = 4² - 4(1)(-1)
= 16 + 4 = 20
Step 3 Apply the formula
x = (-4 ± √20) / 2
Simplify √20 = √(4×5) = 2√5
x = (-4 ± 2√5) / 2
x = -2 ± √5
Answer:
x = -2 + √5 or x = -2 - √5