Answer:
x = -3
Explanation:
Step 1: First, let's find the greatest common factor (GCF) of 4, -8, and -60 and factor it out.
- The GCF of these three numbers is 4, so we can factor it out by dividing each term by 4:
4/4 = 1, -8/4 = -2, and -60/4 = -15.
Thus, the equation we can now use is 4(x^2 - 2x - 15).
Step 2: We can by find the zeroes by factoring.
- Currently, 4(x^2 - 2x - 15) is in standard form, whose general form is ax^2 + bx + c (disregard the 4 for the moment).
- Thus, 1 is our a value, -2 is our b value, and -15 is our c value
- We want to find two numbers whose product equals the product of a and c and whose sum equals b
- We see that -5 form of quadratics, we have 4(x - 5)(x + 3) = 0
- In order to solve for x, we set both terms equal to 0 and solve to find the zeroes of the function:
Step 3: Setting 4(x - 5) equal to 0:
4(x - 5) = 0
x - 5 = 0
x = 5
Setting (x + 3) equal to 0:
x + 3 = 0
x = -3
Thus, the smallest zero is -3