Equations and Solutions

Posted In: Mathematics

Real numbers: a, b, c, p, q, u, v
Solutions: x1, x2,y1, y2, y3

  1. Linear equation with one variable
    $ax+b=0$
    $x=-{b/a}$
  2. Quadratic equation
    $ax^2+bx+c=0$
    $x_{1,2}={-b±√{b^2-4ac}}/{2a}$
  3. Discriminant
    $D=b^2-4ac$
  4. Viete’s formulas
    if $x^2+px+q=0, \then$
    $\{\table x_1+x_2=-p;x_1x_2=q$
  5. if $ax^2+bx=0$, then
    $\{\table x_1=0;x_2=-b/a$
  6. $ax^2+c=0$
    $x_{1,2}=±√{-c/a}$
  7. Cubic equation, Cardano’s formula.
    if $y^3+py+q=0$, then
    $\{\table y_1=u+v;y_{2,3}=-1/2(u+v)±√3/2(u+v)i$
    where
    $u=√^3{-q/2+√{(q/2)^2+(p/3)^2}}$
    and
    $v=√^3{-q/2-√{(q/2)^2-(p/3)^2}}$

Post Tags: Algebra


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