Multiple choice

If a and ß are the roots of the equation x2 – 6x + 6 = 0, what is a3 + ß3 + a2 + ß2 + a+ß equal to?

  1. 150

  2. 138

  3. 128

  4. 124

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

For x² - 6x + 6 = 0 with roots α and β: α+β = 6, αβ = 6. α²+β² = (α+β)² - 2αβ = 36 - 12 = 24. α³+β³ = (α+β)³ - 3αβ(α+β) = 216 - 3(6)(6) = 216 - 108 = 108. Total = α³+β³ + α²+β² + α+β = 108 + 24 + 6 = 138.