math GRE Flashcards
Product of Polynomial Roots
(-1)^n a_0/n
Sum of Polynomial Roots
(-a_n-1)/(a_n)
Root Location Theorem
For real Polynomial p(x) where a,b exist st p(a)<0 and p(b)>0, then there exists a<x<b st p(x) = 0
Rational Roots Theorem
If p(x)=0 has any rational roots, then they must be of the form x=s/t where s is a factor of the constant and t is a factor of the leading coefficient
Complex Radical Roots Theorem
If p(x) has a root of the form x = s + tsqrt(u) where u is not a perfect square, then the conjugate is also a root
Complex Conjugate Roots Theorem
If a complex number is a root, it’s conjugate must be as well
Change of Base Formula
Log_b(a) * log_a(x) = log_b(x)
Tan(a+b)
(tana + tanb) / (1 - tanatanb)
Tan(a-b)
(Tana - tanb)/(1 + tanatanb)
Sin2x
2sinxcosx
Cos2x
Cos^2x - sin^2x
Tan2x
(2tanx) / (1-tan^2x)
Focus of a Parabola
p where y=1/(4p) * x^2
Area of an Ellipse
Piab where x^2/a^2 + y^2/b^2 = 1
Inverse function rule
Derivative of the inverse of f is one over derivative of f