Multiple choice

If α and β are the roots of the equation x2 – 6x + 6 = 0, what is α3 + β3 + α2 + β2 + α + β equal to? यदि समीकरण x2 – 6x + 6 = 0 के मूल α और β है, तो α3 + β3 + α2 + β2 + α + β किसके बराबर है?

  1. 150

  2. 138

  3. 128

  4. 124

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

From x²-6x+6=0: α+β=6, αβ=6. The expression = (α³+β³)+(α²+β²)+(α+β). Using identities: α³+β³ = (α+β)³-3αβ(α+β) = 216-108 = 108. α²+β² = (α+β)²-2αβ = 36-12 = 24. Total = 108+24+6 = 138. This tests Vieta's formulas and algebraic identities.