Answer :
Final answer:
The roots of the quadratic equation 3x² - 6x – 7 = 0 are found using the quadratic formula. The roots simplify to 1 ± √10/3, which do not match with any of the choices provided.
Explanation:
In this mathematics problem, we're asked to find the roots of the quadratic equation 3x2 - 6x – 7 = 0. We can start by employing the quadratic formula, x = [-b ± sqrt(b2 - 4ac)] / (2a).
In our case, a is 3, b is -6, and c is -7. Substitute these into the formula to get -(-6) ± sqrt((-6)2 - 4*3*(-7)) / (2*3). This simplifies to 6 ± sqrt(36+84) / 6, which further simplifies to 6 ± sqrt(120)/6. We can simplify the square root of 120 into 2√30, so the roots are x = [6 ± 2√30] / 6, giving us 1 ± √10/3. Therefore, the roots do not match any of the choices provided.
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