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Answer:
The roots (zeros) of the function are:
Step-by-step explanation:
Given the function
substitute f(x) = 0 to determine the zeros of the function
First break the expression x² + 3x - 40 into groups
x² + 3x - 40 = (x² - 5x) + (8x - 40)
Factor out x from x² - 5x: x(x - 5)
Factor out 8 from 8x - 40: 8(x - 5)
Thus, the expression becomes
switch the sides
Factor out common term x - 5
Using the zero factor principle
if ab=0, then a=0 or b=0 (or both a=0 and b=0)
Solve x - 5 = 0
x - 5 = 0
adding 5 to both sides
x - 5 + 5 = 0 + 5
x = 5
solve x + 8 = 0
x + 8 = 0
subtracting 8 from both sides
x + 8 - 8 = 0 - 8
x = -8
Therefore, the roots (zeros) of the function are: