Find the zeros of the function algebraically. Show all work.
f(x)=x^2-8x+15
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10x
To find the zeros of the function algebraically, we need to find the values of x for which f(x) equals zero.
The function is given by f(x) = (x^2 - 8x + 15) / (10x).
To find the zeros, set f(x) equal to zero:
(x^2 - 8x + 15) / (10x) = 0
First, let's multiply both sides by 10x to clear the fraction:
x^2 - 8x + 15 = 0
Now, we have a quadratic equation. To solve it, we can factor or use the quadratic formula.
Factoring: In this case, we can factor the quadratic equation as follows:
(x - 3)(x - 5) = 0
Setting each factor equal to zero, we have:
x - 3 = 0 or x - 5 = 0
Solving for x, we find:
x = 3 or x = 5
So, the zeros of the function f(x) = (x^2 - 8x + 15) / (10x) are x = 3 and x = 5.