Quadratic functions — A/L Combined Mathematics

How do I practise Quadratic functions?

1 question with a worked solution

1. If α and β are the distinct real roots of the quadratic equation x² - 5x + 3 = 0, what is the exact value of α² + β²?
   1. A) 19
   2. B) 22
   3. C) 25
   4. D) 31
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   Correct answer: A) 19

   From Vieta's formulas for ax² + bx + c = 0: Sum of roots α + β = -b/a = 5, Product of roots αβ = c/a = 3. Using the algebraic identity α² + β² = (α + β)² - 2αβ = (5)² - 2(3) = 25 - 6 = 19.

   Show worked solution

   Step 1: Identify root relationships: α + β = 5, αβ = 3. Step 2: Use identity: α² + β² = (α + β)² - 2αβ. Step 3: Calculate: 5² - 2(3) = 25 - 6 = 19. Answer: 19.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Quadratic functions fit in the syllabus?

Year 1 · Term 1