Multiple choice

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients. $49x^2-81$

  1. $\dfrac {1}{7}, \dfrac {-9}{7}$
  2. $\dfrac {9}{7}, \dfrac {-9}{7}$
  3. $\dfrac {3}{7}, \dfrac {-9}{7}$
  4. $\dfrac {13}{7}, \dfrac {-9}{7}$
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B Correct answer
Explanation

Set 49x^2 - 81 = 0. This is a difference of squares: (7x - 9)(7x + 9) = 0. The solutions are x = 9/7 and x = -9/7.

AI explanation

To find the zeros of the polynomial 49x^2 - 81, set the expression equal to zero so 49x^2 = 81. This is a difference of squares, so it factors into (7x - 9)(7x + 9) = 0. Setting each factor to zero gives 7x - 9 = 0 and 7x + 9 = 0. Solving these simple linear equations yields the zeros x = 9/7 and x = -9/7.

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