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