Two negative, even consecutive integers have a product of 224. Find the smaller integer.
a) -12
b) -14
c) -16
d) -18
Here's a hint:
The square root of 224 is 14.967.
Also -- multiply two consecutive numbers together to see which product is 224.
-16 * -18 is not 224
so im wrong
To find the smaller integer, we need to solve the equation for two negative, even consecutive integers. Let's call the smaller integer x.
The next consecutive even integer will be x + 2, since even numbers are always 2 units apart.
According to the problem statement, the product of these two numbers is 224. We can express this as an equation:
x * (x + 2) = 224
Let's solve this equation:
To begin, expand the equation:
x^2 + 2x = 224
Rearrange the equation to start solving for x:
x^2 + 2x - 224 = 0
Now, we need to factorize this quadratic equation and solve for x:
(x + 16) * (x - 14) = 0
From here, we can either set each factor equal to zero and solve for x or use the zero product property:
x + 16 = 0 or x - 14 = 0
Solving each equation separately:
For x + 16 = 0:
x = -16
For x - 14 = 0:
x = 14
Since we are looking for a negative integer, the smaller integer is -16 (option a).
Therefore, the correct answer is a) -12.