I love the
quadratic equation, don't you? If ax
2 + bx + c = 0, then:
-b + root( b2 - 4ac )
x = -----------------------
2 a
How
aesthetic. Well, anyway, I'm here to talk to you about
quadratics
in disguise! These
little buggers can come up often when you're trying to
solve something, but
you just don't notice! So,
whip out your
TI-83 (with installed
Quadratic equation program) and look at these examples:
(a^4)/2 + a^2 + 1 = 0
You can
rewrite this as u^2 /2 + u + 1 = 0, then
solve for u and take the
square root of those
answers. (Don't forget that a^2 = u has
two answers for every u.
5cos
2(x) + sin(x) - 5 = 0
Which can be
simplified:
-5(1 - cos
2(x)) + sin(x) = 0
-5sin
2(x) + sin(x) = 0
-5u
2 + u = 0
Which you can solve. This actually has some
complicated answers, due to the
sin(x).
5x + 4 / x = 12
Multiply by x and
subtract 12x on both sides:
5x
2 - 12x + 4 = 0
Which is mere child's play.
So, the
quadratic formula shows up in all sorts of nifty (and not so nifty) places. Keep a look out for it, because
it might save your life!