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 hundredths 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 = 01. 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 – 2 = 4

x^2 – x – 6 = 0

(x + 2)(x – 3) = 0

x + 2 = 0 => x = -2 or x – 3 = 0 => x = 32. When the stone hits the ground h(t) = 0. Use the quadratic formula. a = -9.8, b = -10, c = 330x = (10 +/- ((100 – 4(-9.8)(330))^1/2/(2(-9.8)) x = -6.33 or 5.32 (rounded off) The answer is 5.32 seconds.3. a = 3, b = 6, c = -5

b^2 – 4ac = 6^2 – 4(3)(-5) = 36 + 60 = 96

The square root of 96 is irrational, so the equation has two different irrational solutions.

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