Explanation:
To find the zeros of the function f(x), we need to find the values of x that make f(x) equal to zero.
f(x) = (x^2 - 13x + 40)(x^2 - 2x + 3)
Setting f(x) equal to zero, we can use the zero product property to solve for x:
(x^2 - 13x + 40)(x^2 - 2x + 3) = 0
Either (x^2 - 13x + 40) = 0 or (x^2 - 2x + 3) = 0.
Solving for the first equation, we can use the quadratic formula:
x = [13 ± √(13^2 - 4(1)(40))] / 2(1)
x = [13 ± √(169 - 160)] / 2
x = [13 ± √9] / 2
So, the solutions for the first quadratic equation are x = 8 and x = 5.
Solving for the second equation, we can again use the quadratic formula:
x = [2 ± √(2^2 - 4(1)(3))] / 2(1)
x = [2 ± √4] / 2
So, the solutions for the second quadratic equation are x = 1 and x = 2.
Therefore, the zeros of the function f(x) are x = 8, x = 5, x = 1, and x = 2.