Multiple choice

If $\alpha$, $\beta$ are roots of the equation $2x^2-5x+3=0$, then $\alpha^2\beta +\beta^2\alpha$ is equal to?

  1. $15/2$
  2. $-15/4$
  3. $15/4$
  4. $-15/2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the equation 2x^2 - 5x + 3 = 0, the sum of roots alpha + beta = 5/2 and the product alpha * beta = 3/2. The expression alpha^2 * beta + beta^2 * alpha factors to (alpha * beta)(alpha + beta). Substituting the values gives (3/2) * (5/2) = 15/4.

AI explanation

Using the relationships between roots and coefficients for 2 x squared - 5 x + 3 = 0, the sum of the roots is 5/2 and the product is 3/2. We can factor the expression alpha squared beta plus beta squared alpha by taking out the common term alpha beta, leaving alpha beta multiplied by (alpha plus beta). Substituting the known sum and product gives 3/2 multiplied by 5/2, which equals 15/4.

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