Multiple choice

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients. $48y^2-13y-1$

  1. $\dfrac {1}{7}, \dfrac {-1}{16}$
  2. $\dfrac {1}{2}, \dfrac {-1}{14}$
  3. $\dfrac {1}{2}, \dfrac {-1}{11}$
  4. $\dfrac {1}{3}, \dfrac {-1}{16}$
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D Correct answer
Explanation

Solve 48y^2 - 13y - 1 = 0. Using the quadratic formula or factoring: (16y + 1)(3y - 1) = 0. The zeros are y = -1/16 and y = 1/3.

AI explanation

Applying the quadratic formula to 48y^2 - 13y - 1 gives the roots as (13 ± sqrt((-13)^2 - 4(48)(-1))) / 2(48), which simplifies to (13 ± sqrt(361)) / 96 or (13 ± 19) / 96. This calculation yields the two roots as 32/96 and -6/96, which reduce to 1/3 and -1/16.

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