Final answer:
To find the correct value of K such that the quadratic equation 3X^2 + (K-2)X + K+1 = 0 has opposite roots, we need to determine the discriminant of the equation and solve for K.
Step-by-step explanation:
To find the correct value of K such that the quadratic equation 3X^2 + (K-2)X + K+1 = 0 has opposite roots, we need to determine the discriminant of the equation. The discriminant is given by the expression b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, the coefficients are a = 3, b = (K-2), and c = (K+1). Plugging these values into the discriminant formula, we get:
(K-2)^2 - 4(3)(K+1)
We know that for the quadratic equation to have opposite roots, the discriminant must be greater than zero. By setting the discriminant greater than zero and solving for K, we can find the correct value of K that satisfies the condition.