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Multiple choice

If the roots of the equation $x^3+ax^2+bx+c=0$ are in A.P., then $2a^3-9ab= $_____.

  1. $9c$
  2. $18c$
  3. $27c$
  4. $-27c$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If roots are a-d, a, a+d, then sum = 3a = -a (coefficient of x^2), so a = -a/3. Substituting into the cubic equation and using Vieta's formulas leads to the identity 2a^3 - 9ab = -27c.

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