3x^(2)+2x=11 Which of the following describes the solutions to the given equation? Choose 1 answer: A The equation has two distinct rational solutions. B The equation has two distinct irrational solutions. (C) The equation has one distinct real solution. (D) The equation has no real solutions.

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Rewriting the equation: First, we need to rewrite the equation in standard form by moving all terms to one side of the equation. 3x^2 + 2x - 11 = 0Determining factorability: Next, we will determine whether the quadratic equation can be factored easily. If not, we will use the quadratic formula to find the solutions. The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation ax^2 + bx + c = 0.Identifying coefficients: Let's identify the coefficients a, b, and c from our equation. a = 3, b = 2, and c = -11.Calculating the discriminant: Now, we will calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. Discriminant = (2)^2 - 4(3)(-11) = 4 + 132 = 136.Determining the number of solutions: Since the discriminant is positive (136 > 0), we know that there are two distinct real solutions. Now we need to determine if these solutions are rational or irrational.Determining the nature of solutions: The discriminant is not a perfect square, which means the solutions will involve the square root of a non-perfect square number. Therefore, the solutions are irrational.Concluding the solutions: Given that the discriminant is positive and not a perfect square, we can conclude that the equation has two distinct irrational solutions.

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