If A = {x / 6x2 + x – 15 = 0}, B = {x / 2x2 – 5x – 3 = 0}, C = {x / 2x2 – x – 3 = 0}, then find(i) (A ∪ B ∪ C)(ii) (A ∩ B ∩ C)

Sure, let's solve this step by step.

First, we need to find the roots of the equations given in sets A, B, and C.

(i) For set A, the equation is 6x^2 + x - 15 = 0. We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. The roots of this equation are x = 1.5 and x = -1.67.

(ii) For set B, the equation is 2x^2 - 5x - 3 = 0. Again, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. The roots of this equation are x = 3 and x = -0.5.

(iii) For set C, the equation is 2x^2 - x - 3 = 0. We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. The roots of this equation are x = 1.5 and x = -1.

Now, we can find the union and intersection of these sets.

(i) The union of sets A, B, and C, denoted as A ∪ B ∪ C, is the set of all elements that are in A, or in B, or in C. So, A ∪ B ∪ C = {-1.67, -1, -0.5, 1.5, 3}.

(ii) The intersection of sets A, B, and C, denoted as A ∩ B ∩ C, is the set of all elements that are common to A, B, and C. So, A ∩ B ∩ C = {1.5}.