Final answer:
The original question about the value of 'a' cannot be answered due to missing information. The examples and explanation provided illustrate how one would typically find 'a' when a factor of a polynomial is known and the procedure for solving a quadratic equation using the quadratic formula.
Step-by-step explanation:
The question is incomplete as it does not provide the full expression in which 3x + 4 is a factor, nor does it mention how 'a' is related to this expression. Typically, if you know that 3x + 4 is a factor of some polynomial expression, we would set it to zero to find the roots of the expression, implying 3x + 4 = 0. If we were solving for x, we would get x = -4/3. However, without the complete polynomial, we cannot solve for 'a'.
Let's look at a different example to demonstrate how we would find 'a' if we had a complete polynomial. Suppose we had the polynomial P(x) = 3x² + ax + 12 and we knew that 3x + 4 was a factor. We would set the factor equal to zero and solve for x, which yields x = -4/3. We then substitute x back into the polynomial to solve for 'a': P(-4/3) = 3(-4/3)² + a(-4/3) + 12 = 0. Simplifying and solving for a would give us the value we're looking for.
Exercise 2.4.2 asks for answers in scientific notation with appropriate significant figures. For instance, part a, which is 217 ÷ 903, would be calculated and then written in scientific notation considering significant figures.
The expression from another part of the question, 3.59, seems to refer to a quadratic equation of the form at² + bt + c = 0. To solve for the roots, you would use the quadratic formula, which requires the values of a, b, and c. These values must be provided to complete the problem.