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Mary used the quadratic formula to find the zeros of the equation below. Select the correct zeros of the equation:3x^2 - 9x + 2 = 0Answer choices include:x = fraction numerator 9 plus-or-minus square root of 57 over denominator 6 end fractionx equals fraction numerator negative 9 plus-or-minus square root of 57 over denominator 2 end fractionx equals fraction numerator 9 plus-or-minus square root of 105 over denominator 2 end fractionx equals fraction numerator negative 9 plus-or-minus square root of 105 over denominator 6 end fraction

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Final answer:

To find the zeros of the quadratic equation 3x^2 - 9x + 2 = 0, we apply the quadratic formula, x = \([-b \pm \sqrt{b^2 - 4ac}\]) / (2a), with a = 3, b = -9, and c = 2 to get x = \([9 \pm \sqrt{57}\]) / 6. Thus, the correct zeros are x = (9 ± √57) / 6.

Step-by-step explanation:

The correct zeros of the quadratic equation 3x^2 - 9x + 2 = 0 can be found using the quadratic formula, which is given for any quadratic equation in the form ax^2 + bx + c = 0 as:

x = \([-b \pm \sqrt{b^2 - 4ac}\]) / (2a)

In this case, a = 3, b = -9, and c = 2. Plugging these values into the quadratic formula and simplifying gives:

x = \([9 \pm \sqrt{(9)^2 - 4*3*2}\]) / (2*3)

x = \([9 \pm \sqrt{81 - 24}\]) / 6

x = \([9 \pm \sqrt{57}\]) / 6

Therefore, the correct zeros of the equation are:

x = fraction numerator 9 plus-or-minus square root of 57 over denominator 6 end fraction

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