The Purplemath Forums

As written, this looks like the quadratic: -5x^2 + 4x + 6 = 0 But quadratic equations have at most two real solutions. You list four roots. This leads me to think there is a typo in your equation and that it should be: x^4 - 5x^2 + 6 = 0 . Since this is a quartic, it can indeed have four solutions. ...

Hi Jesse, A little easier in this case for the quartic. Define a new variable, such as u = x^2. Then u^2 = x^4. So now the equation can be written as: u^2 - 5u + 6 = 0. This is quadratic in u, and factorable. Solve for u. Then substitute x^2 into your solutions and solve the resulting two quadratics...

The half-meter is added to each end. So 5 + 1/2 + 1/2 = 6.

Do you ever enlist help with the lessons?

Interesting. According to one of the online dictionaries that I just consulted, when either is used as an adjective (as in this case) it can mean 1. Any one of two; one or the other: wear either coat. 2. One and the other; each: rings on either hand. So you interpreted it in the first sense, and I i...

Do you invite/welcome suggestions for edits (formatting, presentation, etc.) from qualified individuals? Or are such interlopers frowned upon?

For whatever reason, your equation is not rendering on my machine. How did you type it in?

I oriented my triangles with the side b along the horizontal (the initial side of angle A), and the side c as the terminal side. Then, drop a perpendicular line from the end of c down to the line that b sits on. It shouldn't take long for you to determine that the length of this vertical line is c s...

In order to find the surface area of the sphere, you need to find know its radius. You will use the cube to determine the radius of the sphere. Since the cube is inscribed in the sphere, the center of the cube and the center of the sphere coincide. Also, since the cube is inscribed inside the sphere...

Well...graphing it showed me there are 6 points that solve the system. Can you first determine the intersection of the plane and the sphere? It's a circle, and if you can get the equation for that you can then work on finding the intersection of the circle with the cube-like 4th degree.