Multiple choice

The roots α, β of the equation 3x2 + λx - 1 = 0, satisfy 1 α 2 + 1 β 2 = 15. The value of ( α3 + β3)2, is

  1. 16

  2. 4

  3. 1

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Interpreting the garbled condition as 1/alpha^2 + 1/beta^2 = 15, use alpha beta = -1/3. This gives alpha^2 + beta^2 = 5/3 and therefore (alpha + beta)^2 = 1. Then alpha^3 + beta^3 = (alpha + beta)^3 - 3alpha beta(alpha + beta) = 2(alpha + beta), whose square is 4.

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