Multiple choice

Find a quadratic equation each with the given numbers as the sum and product of its zeroes respectively. $\dfrac {-10}{\sqrt 3}, 7$

  1. $3x^2-11\sqrt3x+21=0$
  2. $3x^2-17\sqrt2x+21=0$
  3. $3x^2+10 \sqrt3 x+21=0$
  4. $3x^2-15x+21=0$
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C Correct answer
Explanation

For a quadratic equation with sum of roots S and product of roots P, the equation is x^2 - Sx + P = 0. Here S = -10/sqrt(3) and P = 7, so x^2 - (-10/sqrt(3))x + 7 = 0. Multiplying by 3 gives 3x^2 + 10sqrt(3)x + 21 = 0.

AI explanation

The standard form of a quadratic equation is derived from its zeros using the formula x^2 - (sum of zeros)x + (product of zeros) = 0. Substituting the given sum of -10/sqrt(3) and product of 7 into this formula yields x^2 + 10x/sqrt(3) + 7 = 0. To clear the denominator in the x coefficient, multiply the entire equation by 3. The resulting equation is 3x^2 + 10*sqrt(3)x + 21 = 0.

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