Multiple choice

Find a quadratic equation each with the given numbers as the sum and product of its zeroes respectively. $-\sqrt 3, \dfrac {1}{4}$

  1. $2x^2+4\sqrt 3x+4$
  2. $x^2-4\sqrt 3x+4$
  3. $4x^2+4\sqrt 3x+1$
  4. $2x^2+4\sqrt 3x+1$
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C Correct answer
Explanation

Quadratic equation: x^2 - (sum of zeroes)x + (product of zeroes) = 0. x^2 - (-sqrt(3))x + 1/4 = 0. x^2 + sqrt(3)x + 1/4 = 0. Multiply by 4: 4x^2 + 4sqrt(3)x + 1 = 0.

AI explanation

A quadratic equation can be constructed from the sum and product of its zeros using the formula x^2 - (sum)x + (product) = 0. Plugging in the sum of -sqrt(3) and the product of 1/4 gives the equation x^2 + sqrt(3)x + 1/4 = 0. To eliminate the fraction, multiply the entire equation by 4. This results in the quadratic equation 4x^2 + 4*sqrt(3)x + 1 = 0.

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