Final answer:
The coefficients a, b, and c from the quadratic equation 3x² − 2x + 7 = 0 are substituted into the quadratic formula as 3, -2, and 7, respectively, to calculate the roots.
Step-by-step explanation:
The quadratic equation given in the question is 3x² − 2x + 7 = 0. This equation is already in the standard form ax² + bx + c = 0, where a, b, and c are coefficients and represent constants. Using the quadratic formula x = −b ± √(b²-4ac) / (2a), we can substitute the coefficients directly. For the given equation, a = 3, b = -2, and c = 7. Substituting these into the quadratic formula, we get: x = (−2)(-2) ± √((-2)²-4(3)(7)) / 2(3).
This shows the coefficients were correctly substituted into the quadratic formula to find the roots of the quadratic equation. The equation 3x² − 2x + 7 = 0 is in standard form. In the quadratic formula, the coefficients a, b, and c are substituted as follows: a = 3, b = -2, and c = 7. Substituting these values into the quadratic formula gives: x = (-b ± √(b² - 4ac)) / (2a). So the equation with the coefficients correctly substituted into the quadratic formula is: x = (-(-2) ± √((-2)² - 4*3*7)) / (2*3)