Multiple choice

Find a quadratic polynomial whose sum and product respectively of the zeros, are $\dfrac {-3}{2\sqrt 5}, -\dfrac {1}{2}$ .

  1. Polynomial: $x^2+3\sqrt{5}x-7\sqrt{5}$
  2. Polynomial: $2\sqrt{5}x^2+3x-\sqrt{5}$
  3. Polynomial: $2x^2-7\sqrt{5}x-3\sqrt{5}$

  4. None of these
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B Correct answer
Explanation

A quadratic polynomial is given by x^2 - (sum of zeros)x + (product of zeros). Here, x^2 - (-3/(2*sqrt(5)))x + (-1/2) = x^2 + 3/(2*sqrt(5))x - 1/2. Multiplying by 2*sqrt(5) gives 2*sqrt(5)x^2 + 3x - sqrt(5).

AI explanation

A quadratic polynomial can be formed using the formula x^2 - (sum of zeros)x + (product of zeros). Substituting the sum of -3 / (2*sqrt(5)) and the product of -1/2 yields x^2 + 3x / (2*sqrt(5)) - 1/2. To clear the denominators, multiply the entire polynomial by 2*sqrt(5). This multiplication results in the final polynomial 2*sqrt(5)x^2 + 3x - sqrt(5).

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