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Find the zeroes of the polynomial 3x²-2root3+1

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We can use the quadratic formula to find the zeroes of the given polynomial. The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± sqrt(b² - 4ac)) / 2a

Comparing this to the given polynomial, we see that a = 3, b = -2√3, and c = 1. Substituting these values into the quadratic formula, we get:

x = [(-(-2√3)) ± sqrt((-2√3)² - 4(3)(1))] / 2(3)

x = [(2√3) ± sqrt(12 - 4)] / 6

x = [(2√3) ± sqrt(8)] / 6

x = [(2√3) ± 2√2] / 6

x = (√3 ± √2) / 3

Therefore, the zeroes of the polynomial 3x² - 2√3x + 1 are (√3 + √2) / 3 and (√3 - √2) / 3.

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