To find the zeroes of the function fx = x² – 6x + 8, we need to set the equation equal to zero:
x² – 6x + 8 = 0
This is a quadratic equation, and we can solve for x using factoring. We look for two numbers that multiply to 8 (the constant term) and add up to -6 (the coefficient of x). The numbers -2 and -4 fit these criteria, since:
- -2 * -4 = 8
- -2 + -4 = -6
Therefore, we can factor the equation as follows:
(x – 2)(x – 4) = 0
Setting each factor equal to zero gives us:
- x – 2 = 0 → x = 2
- x – 4 = 0 → x = 4
So, the zeroes of the function are x = 2 and x = 4.