Multiple choice

If α and β are the roots of the equation Ax2 - Bx + C = 0 and α- β = 4, then which of the following is TRUE ?

  1. B2-10A2=4AC+ 4B2

  2. B2-10A2=4AC+6A2

  3. B2-8A2=4AC+10A2

  4. B2-16A2=4AC+10A2

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For Ax² - Bx + C = 0 with roots α, β: α+β = B/A, αβ = C/A. Given α-β = 4, so (α-β)² = 16 = α² + β² - 2αβ. Using α² + β² = (α+β)² - 2αβ = B²/A² - 4C/A. So 16 = B²/A² - 4C/A. Multiplying by A²: 16A² = B² - 4AC. Simplifying option B: B² - 10A² = 4AC + 6A² gives B² - 16A² = 4AC ✓.