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False 18:03:452018-11-05 15:47:28Coachella 2017 - 5.24.2017 / Bruhaha / A Look Back at 2017
Coachella is coming up this weekend, and we’ve got you covered with some quick and dirty Coachella recs: here’s what we’re listening to before heading to the desert.
2017 will be a tough year for many Coachella attendees. First, the line-up’s missing Kanye West, and his not-so-good-year. Then, as the festival season is getting underway, that we’re still suffering from the after-effects of the Sandy Hook shooting and all of its aftermath in both the US and the world.
In this episode, NFT favorite, Kyle D.J, talks about how this season will be bittersweet for him. Additionally, Alex Shearer (@thealexsheets) and Joe (@SIDE_ARMS) talk about all the ups and downs of the festival season, as well as what a festival can and should be.
If you’re heading out to Coachella this weekend, we hope this episode helps with your preparations.Q:
Determine the Real-Valued Roots of the Quartic Equation $x^4 + 3x^3 + x + 1= 0$
Consider the equation $x^4 + 3x^3 + x + 1= 0$
This has the complex roots $a+bi, a-bi, a-bi, -a+bi$ where $a,b \in \mathbb{R}$
How can you prove the following?
1) If $a = 1, b = 0$ then the equation $x^4 + 3x^3 + x + 1 = 0$ can be written as $x(x+1)(x-1)(x^2 + 1) = 0$
Why do we know this?
2) What if $a = \frac{1}{2}$, $b = \frac{1}{2}$?
A:
For the first case:
$
x^4 + 3x^3 + x + 1 = 0
$
$
\left(x^2 + \frac{3}{2}x + 1\right)^2 - x^2 = 0
$
which is the same as
$
x^2 + \left(x^2 - \frac{1}{4}\right) + 1 = 0.
$
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