Multiple choice

Find the quadratic polynomials whose zeroes are

  1. 3, -5

  2. 5, -5

  3. -9, 1/9
  4. $3 + \sqrt 5 $, $3 - \sqrt 5 $
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AI explanation

Using the sum and product of zeros formula, if the zeros are 3 and -5, their sum is (3) + (-5) = -2 and their product is (3)(-5) = -15. The required quadratic polynomial is formed as x^2 - (sum of zeros)x + (product of zeros), which results in x^2 - (-2)x + (-15) or x^2 + 2x - 15. Therefore, the pair of zeros matching the required polynomial setup is 3 and -5.

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