Multiple choice

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients. $63-2x-x^2$

  1. $7, 3$
  2. $7, 7$
  3. $7, -9$
  4. $7, -2$
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C Correct answer
Explanation

The polynomial is -x^2 - 2x + 63. Setting it to zero gives x^2 + 2x - 63 = 0, which factors into (x + 9)(x - 7) = 0. Thus, the zeros are 7 and -9.

AI explanation

Rewriting the polynomial as x^2 + 2x - 63 = 0 and applying the quadratic formula yields x = (-2 ± sqrt(2^2 - 4(1)(-63))) / 2(1). This simplifies to (-2 ± sqrt(256)) / 2, giving (-2 ± 16) / 2. The resulting roots are 14/2 and -18/2, which are 7 and -9.

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