meaningful. This will be shown in some problems. In that case, disregard the
solution that does not make sense. (Note:Sometimes the two solutions are
equal to each other; in that case there is only one solution.)
EXAMPLE:If the sum of two numbers is 20 and the product of the two
numbers is 36, find the numbers.
SOLUTION:
GOAL: You are being asked to find two numbers whose sum is 20 and whose
product is 36.
STRATEGY: Letx¼one number
and 20x¼the other number
If the product of the two numbers is 36, the equation isx(20x)¼36.
IMPLEMENTATION: Solve the equation:
xð 20 xÞ¼ 36
20 xx^2 ¼ 36
0 ¼x^2 20 xþ 36
0 ¼ðx 18 Þðx 2 Þ
x 18 ¼ 0 x 2 ¼ 0
x 18 þ 18 ¼ 0 þ 18 x 2 þ 2 ¼ 0 þ 2
x¼ 18 x¼ 2
Hence the two numbers are 18 and 2.
EVALUATION: Check the facts of the problem. The sum 18þ2 is 20 and
the product 18 2 ¼36.
EXAMPLE:If the product of two consecutive numbers is 306, find the
numbers.
LESSON 19 Using Quadratic Equations 233