Multiple choice

Find the sum and product of the roots of the equation $\sqrt{3}x^{2}+27x+5\sqrt{3}=0$

  1. $-9\sqrt{3},5$
  2. $9\sqrt{3},5$
  3. $6\sqrt{3},-5$
  4. $6\sqrt{3},5$
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A Correct answer
Explanation

For ax^2 + bx + c = 0, sum of roots = -b/a, product = c/a. Here a=sqrt(3), b=27, c=5sqrt(3). Sum = -27/sqrt(3) = -9sqrt(3). Product = 5sqrt(3)/sqrt(3) = 5.

AI explanation

We compare the given expression sqrt(3)*x^2 + 27*x + 5*sqrt(3) = 0 to the standard quadratic form ax^2 + bx + c = 0 to get a = sqrt(3), b = 27, and c = 5*sqrt(3). Using the sum of roots formula, the sum is -b/a = -27/sqrt(3) = -9*sqrt(3). Using the product of roots formula, the product is c/a = 5*sqrt(3)/sqrt(3) = 5. Therefore, the sum and product are -9*sqrt(3) and 5 respectively.

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