Multiple choice

lf $\alpha,\beta,\gamma,\delta$ are the roots of the equation $3x^{4}-8x^{3}+2x^{2}-9=0$, then $\Sigma\alpha\beta=$

  1. $\displaystyle \frac{2}{3}$
  2. $\displaystyle \frac{-2}{3}$
  3. $\displaystyle \frac{8}{3}$
  4. $\displaystyle \frac{-8}{3}$
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A Correct answer
Explanation

For a polynomial equation of the form ax^4 + bx^3 + cx^2 + dx + e = 0, the sum of the products of the roots taken two at a time is given by c/a. In the given equation, a = 3 and c = 2, so the sum of the products of the roots is 2/3.

AI explanation

For the polynomial 3x^4 - 8x^3 + 2x^2 + 0x - 9 = 0, Vieta's formulas state that the sum of the products of the roots taken two at a time equals e2/a4. Here, the coefficient a4 is 3 and the coefficient of x^2, which represents e2, is 2. Therefore, the sum alpha*beta equals 2 divided by 3.

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