Final answer:
The zeroes of the function f(x)=x²+6x+8 are -5 and -1.
Step-by-step explanation:
The zeroes of the function f(x)=x²+6x+8 can be found by setting f(x) equal to zero and solving for x. In this case, we have:
x²+6x+8 = 0
To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b²-4ac))/(2a)
Here, a = 1, b = 6, and c = 8. Plugging these values into the quadratic formula, we get:
x = (-6 ± √(6²-4*1*8))/(2*1)
Simplifying further, we have:
x = (-6 ± √(36-32))/(2)
x = (-6 ± √4)/(2)
Therefore, the zeroes of the function are:
smaller x = -3 - √4 = -5
larger x = -3 + √4 = -1