metadata
source: knowledge_base
topic: algebra
class_level: class_10
difficulty: intermediate
Algebra and Number Theory: Quadratic: x=(-b±sqrt(b^2-4ac))/2a. D=b^2-4ac. D>0: two real roots. D=0: repeated root. D<0: complex roots. log(ab)=log(a)+log(b). log(a^n)=nlog(a). a^2-b^2=(a+b)(a-b). a^3+b^3=(a+b)(a^2-ab+b^2). AP: S_n=n/2(2a+(n-1)d). GP: S=a(1-r^n)/(1-r). Infinite GP: a/(1-r) for |r|<1.