1.) In solving the equation (x + 1)(x - 2) = 4, Eric stated that the solution would be x + 1 = 4 => x = 3 or (x - 2) = 4 => x = 6. However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.
2.) If a stone is tossed from the top of a 330 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 - 10t + 330, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth's place; include units in your answer.
3.) Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
3x^2 + 6x - 5 = 0
1. Eric should be making use of the Zero Product Theorem, but for that to work the product of his two factors must be 0. Here is the correct solution.
x^2 - x ...
The expert solves an equation. The nearest hundredths place are provided.