f(x)=x^2-9x+14/4x find the zeros of the function?

Question

I know once you factor out the top it would be (x-7)(x-2)/4x but how do you find the zeros from there?

Answer 1

(x-7)(x-2)/4x = 0

(x-7)/4x = 0
x-7 = 0
x = 7

(x-2)/4x = 0
x-2 = 0
x = 2

Answer 2

If you can get that far.... you solve this equation.

(x-7)(x-2)/4x = 0

If you stop and think a moment... if your formula is AB=0, then you can make either A or B to zero and the equation is valid, correct? Then, in your case, you'd make (x-7) or (x-2) to zero. Obviously, x=7 or x=2 is the answer.

Whatabout 4x? Nothing for this case. There is no value you can plug into x to make this whole equation to zero. If you plug in zero to x, then you get 4x=0. You cannot have divide by zero equal to zero.

It'd be little different if your formula is something like:
f(x)=x(x-2)/4x

You can initially say x=0 or x=2, but if you make x=0, then denominator becomes zero and the whole formula becomes invalid. (you cannot divide by zero), so the answer for this one is x=2, and NOT x=0

Answer 3

(x-7)(x-2)/4x = (1/4x)(x-7)(x-2)

(1/4x)(x-7)(x-2) = 0

1/4x = 0 or x-7 = 0 or x-2 = 0

no solution, x = 7, or x = 2

So 7 & 2 are the zeroes

Try graphing on a graphing calculator to see the graph
crosses the x axis at 2 & 7