Multiple choice

Find a quadratic equation each with the given numbers as the sum and product of its zeroes respectively. $\dfrac {-2\sqrt 5}{3}, -\dfrac {5}{3}$

  1. $3x^2+4\sqrt 5x-5=0$
  2. $3x^2+2\sqrt 5x-5=0$
  3. $3x^2+3\sqrt 5x-5=0$
  4. $3x^2+7\sqrt 5x-5=0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A quadratic equation is x^2 - (sum)x + (product) = 0. Here, x^2 - (-2sqrt(5)/3)x + (-5/3) = 0. Multiplying by 3 gives 3x^2 + 2sqrt(5)x - 5 = 0.

AI explanation

To form a quadratic equation from the sum and product of its zeros, use the standard formula x^2 - (sum of zeros)x + (product of zeros) = 0. Substituting the sum of -2*sqrt(5)/3 and the product of -5/3 gives the equation x^2 - (-2*sqrt(5)/3)x + (-5/3) = 0. Simplifying the signs results in x^2 + 2*sqrt(5)x/3 - 5/3 = 0. Multiplying the entire equation by 3 to clear the denominators results in the final quadratic equation 3x^2 + 2*sqrt(5)x - 5 = 0.

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