Final answer:
The given quadratic equation can be solved using the quadratic formula, resulting in a negative root and a positive root x = 7.2 x 10^-2. Since negative roots often do not make sense in practical problems, such as concentrations in chemistry, only the positive root is considered correct. The initial proposed solutions do not match the calculated one.
Step-by-step explanation:
The student's question involves solving a radical equation and verifying the solutions. In this context, the given equation x² + 1.2 x 10-2x - 6.0 × 10-3 = 0 appears to be a quadratic equation that can be solved using the quadratic formula. The general form of a quadratic equation is ax² + bx + c = 0, and the solution can be found by applying the quadratic formula:
x = ∛(-b ± √(b² - 4ac)) / (2a)
For our specific equation, the coefficients are a = 1, b = 1.2 × 10-2, and c = -6.0 × 10-3. Upon solving, we find that the equation yields one negative root and one positive root. Since a negative root does not make sense in the context of the problem (which could be related to concentration in a chemistry problem), we consider only the positive root:
x = 7.2 × 10-2
When solving simultaneous equations or equations with radicals, it is crucial to eliminate terms wherever possible to simplify the algebra, and then carefully check and recheck the solutions to ensure they are reasonable. Furthermore, understanding how to work with roots, such as square roots or cube roots, is essential when dealing with certain equilibrium problems in subjects like Chemistry.
It is important to note that the provided solution options (a) x=1, (b) x=2, (c) x=-1, and (d) x=3 do not contain the calculated solution x = 7.2 × 10-2. Therefore, none of the initial proposed solutions is correct according to the actual equation provided.