Calculus-Based Physics by Jeffrey W. Schnick - HTML preview

Chapter 1 Mathematical Prelude

equation. The second multiplicand in the expression (a x + b)x = 0 is x itself, so

x = 0

is a solution to the equation. Setting the first term equal to zero gives:

a x + b = 0

a x = −b

b

x = −

a

Now suppose the b in the quadratic equation

2

a x + bx + c = 0 , equation 1-8, is zero. In that case,

the quadratic equation reduces to:

2

a x + c = 0

which can easily be solved without the quadratic formula as follows:

a x2 = −c

2

c

x = −

a

c

x = ± −

a

where we have emphasized the fact that there are two square roots to every value by placing a

plus-or-minus sign in front of the radical.

Now, if upon arranging the given equation in the form of the quadratic equation (equation 1-8):

2

a x + bx + c = 0

you find that a, b, and c are all non-zero, then you should use the quadratic formula. Here we

present an example of a problem whose solution involves the quadratic formula:

7