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

Solution Preview

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 ...

Solution Summary

The expert solves an equation. The nearest hundredths place are provided.

... Solution: ... The equation changes to. ...x 2 + x = −2 => x 2 + x = 4 => x 2 + x − 4 = 0 − 1 ± 1 − 4(1)( −4) − 1 ± 17 => x = = 2 2 Or x2 + x = 1 => x 2...

... 11 X + 4 2 9) solve X + 12 X + 32 = 0 2 10) solve X + 5 X 9 = 0 2 11) Graph the quadratic equation after completing the given table of values. Y = X 1. ...

... square root of the number on the right side of the equation and solve for x Example: Solve x2 + 3x ... 2x + 3 = 7 2x + 3 = 7 2x = 4 2x = -10 x = 2 x = -5 Try ...

...1. Find the particular solution of the differential equation that satisfies ... 8)dx , y(1) = 2 A) y = x ln | x | 6 x + 8 y = 8 x ln | x | +4 x − 2 B) C ...

... And the solution to the heat equation is: n (- 1) -1 ¥ ¥ - n 2t 2 u (x , t ) = sin (nx ) = e - nt sin (nx ) å å (1.28) C ne ( ) n n2 - 4 n=1 n=1. ...

Solving system of equations by graphing. Solve each system of equations by graphing: 1). y=x-4 and y= -2x+2. 2). Y=2x-3 and y=-x-6. 3). Y=3x-2 and y=1/2x+5. ...

...solve for y: 0 + 4 y = −2 −2 y= 4 1 y=− 2 To solve for x, we will substitute y in either of the simplified equations. We choose equation 1: 1 2x ...

...4. Solve the trigonometric equation (sin x)(2cos x − 1) = 0 in the interval [0, 360°). (a) Find the exact value of arccos sin( 3π/ 2 ) (b) Find the exact ...

... Put this value of x in equation 2 1 − 12 ... 8 y + 8 y = 32 − 32 = 32 We Land up with a false statement meaning thereby system does not have any solution. ...

... y = 2x - 1 y = 2*4 - 1 = 8 - 1 = 7 The solution is x = 4, y = 7 The system is independent. 38.) Y= -4x -7 Y= 3x Replace by value of y in second equation by y ...