Algebra Demystified 2nd Ed

366 alGEbra De mystif ieD

The quadratic formula can be messy to compute when any of a, b, or c is a

fraction or decimal. We can get around this difficulty by multiplying both sides

of the equation by the LCD or some power of 10. This would leave us with a,

b, and c as integers (whole numbers or their negatives). To see how this step can

save time, we will plug values for a, b, and c without clearing the fractions and

then we will clear the fractions, allowing us to plug in simpler values.

EXAMPLE

Evaluate the quadratic formula.

1

2

1

2

xx^2 −−= 10

We use a = ^1

2

, b = –^1

2

, c = –1 in the quadratic formula.

x bbac

a

=−±^ −^

(^24)
2
x=
−−



±−



− 



−


1
2
1
2
41
2
1
21
2
2
 ()
 
Simplifying this expression would require several steps. Let us see how
simple the formula looks after we have cleared the fractions in the original
equation. We now eliminate the fractions by multiplying both sides of the
equation by 2.
2 1
2
1
2
 xx (^2) −− 120



= ()
x^2 − x − 2 = 0
With the fractions cleared, we can use the quadratic formula with more
convenient values: a = 1, b = –1 and c = –2
x=−− ±−−−() () ()()
()
1141 2
21
2
EXAMPLE
Evaluate the quadratic formula.
EXAMPLE
Evaluate the quadratic formula.