Multiple choice

If 2 and $-\dfrac {1}{2}$ as the sum and product of its zeros respectively then the quadratic polynomial f(x) is

  1. $x^2-2x-4$
  2. $4x^2-2x+1$
  3. $2x^2+4x-1$
  4. $2x^2-4x-1$
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D Correct answer
Explanation

A quadratic polynomial is given by x^2 - (sum)x + (product). Here, x^2 - 2x - 1/2. Multiplying by 2 to clear the fraction gives 2x^2 - 4x - 1.

AI explanation

Using the relationship between zeros and coefficients, a quadratic polynomial is given by k(x^2 - (Sum of zeros)x + Product of zeros). Substituting the sum as 2 and the product as -1/2 gives f(x) = k(x^2 - 2x - 1/2). To eliminate the fraction, multiply the expression by 2 (meaning k = 2) to get f(x) = 2x^2 - 4x - 1.

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