quadratic equation is an equation with unknown variable to the
standard form of a quadratic equation is
a, b, and c are constants and x
is the unknown variable.
equation is not in standard form, we must manipulate it until it
we set y = 0 in any function, we are finding the x–intercept(s)
for that function.
So when we
solve a quadratic in the form we are really finding the x–intercepts.
are also called roots.
term for roots or x-intercepts is zeros.
we solve a quadratic in the standard form we are finding the
roots of the function.
and zeros are very important in electronics and control
There are a variety of
techniques for solving quadratic equations including:
Using the quadratic formula; Completing the square; Using a
We will discuss the first
two techniques only.
Solving by Factorization
A number is said to be
factorized when it is written as a product.
For example 24 can be
factorized into 8 ´
3. Algebraic expressions
can also be factorized, as given
Solving Using a Formula
all quadratics can be factorized. Accordingly, we will present the
quadratic formula for solving the above equation. The quadratic
the following quadratic equation
of constants are: a = 1, b = 5, and c =
values can be substituted into the quadratic formula to give
two values of x:
one corresponds to the + sign and the second one correspond to
the – sign. The answer is
values satisfy the original equation.
bending moment of a beam M, is given by the equation
x is the distance (m) along a beam from one end. Find
the value of x for which M = 0.
Solution: We have
use to determine x.
of constants are: a = 7, b = 4, and c =
-3, which can be substituted into the quadratic equation to
are two values of x:
first one corresponds to the + sign and the second one
correspond to the – sign.
we cannot have a distance of -1.00 on the beam, the bending
moment M = 0 is at x = 0.429 m.