SOLUTION: One integer is 8 less than 5 times another. Their product is 21. Find the integers.

Question 950499: One integer is 8 less than 5 times another. Their product is 21. Find the integers.
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
a and b are integers
a*b=21
a=21/b
a=5b-8 Substitute for a
21/b=5b-8 Multiply each side by b
21=5b^2-8b Subtract 21 from each side.
0=5b^2-8b-21

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=484 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3, -1.4. Here's your graph:

The integer answer is 3 so ANSWER: One of the numbers is 3.
a=21/b=21/3=7 ANSWER 2: The other integer is 7.
CHECK:
a=5(b)-8
7=5(3)-8
7=15-8
7=7
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