Multiple choice

Find the zeros of the following quadratic polynomial and verify the basic relationships between the zeros and the coefficients. $x^2-2x-8$

  1. $(4, -2)$   
  2. $(4, 2)$   
  3. $(-4, -2)$   

  4. None of these
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A Correct answer
Explanation

The polynomial x^2 - 2x - 8 factors into (x-4)(x+2). Setting this to zero gives roots x=4 and x=-2.

AI explanation

We find the zeros of the polynomial x^2 - 2x - 8 by splitting the middle term, rewriting it as x^2 - 4x + 2x - 8 = 0. Factoring by grouping gives x(x - 4) + 2(x - 4) = 0, which leads to (x - 4)(x + 2) = 0. Setting each factor to zero gives the roots x = 4 and x = -2. The zeros of the polynomial are (4, -2).

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