• Quadratic Equations

    Quadratic Equations are equations of the second degree. The standard form of a quadratic equation is a.X2 + b.X + c = 0 where X represents the unknown, a,b and c are constants numerical values and a ≠ 0. a and b are also known as the quadratic coefficient and linear coefficient respectively. Quadratic Equations can be solved by:
    Factorization, completing the square, quadratic formula and Graphing. When solved, a quadratic equation will have two solutions (known as its roots), which may or may not be distinct or they may or may not be real.

    Discriminant (D)

    The discriminant -represented by the letter D or the Greek letter Δ- of a quadratic equation is the part of the quadratic formula which is underneath the √ sign, which is: D = b2 - 4ac.
    This formula is used to determine the number and nature of the roots of the quadratic equation. There are three possible results from the discriminant equation, these are:
    1 - b2 - 4ac > 0. If the discriminant is positive, there are two distinct roots.
    2 - b2 - 4ac = 0. If the discriminant is zero, there is exactly one real root.
    3 - b2 - 4ac < 0. If the discriminant is negative, there are no real roots, rather there are two none real roots which are known as complex roots.
    The figure to the far right shows the different parts of the quadratic curve. The figure to the right gives the three possible curves for a positive quadratic equation. For a negative quadratic equation, all curves are reflected on the X-axis.
    The following program shows how a quadratic equation can be solved using factorization and the quadratic formula.

    Quadratic Equation Formulae


    Quadratic Discriminant
    Quadratic Curve

Factorization Tool

Use this tool to factorize quadratic equations. The quadratic equation must be in the general form:
a.X2 + b.X + c = 0 where a ≠ 0, b & c can be 0;

  Enter the values of the constants a,b and c below

  The coefficient of X2, a:
  The coefficient of X, b:
  The constant, c:
 

Steps to solve the equation

Step 1, Find the factors of a (the coefficient of X2).

Step 2, Find the factors of the constant c.

Step 3, Choose two factors of a, from (Step 1) which, when multiplied together give a.

Step 4, Choose two factors of c, from (Step 2) which, when multiplied together give c and when cross-multiplied by the factors of a, from (Step 3), give b, the coefficient of X.

Step 5, From the criss-cross multiplication, create two brackets. Make each bracket = 0 to find the value of X.
See Graphical Illustration to the right.

Factorization

Results