Multiple choice

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients. $6x^2-x-1$

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

Setting 6x^2 - x - 1 = 0, we factor it as (3x+1)(2x-1) = 0. The zeros are x = -1/3 and x = 1/2.

AI explanation

To find the zeros of the polynomial 6x^2 - x - 1, we apply the quadratic formula, x = (-b ± sqrt(b^2 - 4ac)) / 2a. Substituting a = 6, b = -1, and c = -1 gives x = (1 ± sqrt((-1)^2 - 4(6)(-1))) / 12, which simplifies to (1 ± 5) / 12. This yields the two roots as 6/12 and -4/12, which are 1/2 and -1/3.

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