Quadratic Equations
Quadratic Equations are equations of the second degree. The standard
form of a quadratic equation is a.X^{2} + 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 = b^{2} - 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 - b^{2} - 4ac > 0. If the discriminant is positive,
there are two distinct roots.
2 - b^{2} - 4ac = 0. If the discriminant is zero, there
is exactly one real root.
3 - b^{2} - 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.