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To find the zeros of the function, 

f(x) = - 4x + 6,

the number of possible zeros are to be found out.

The largest exponent of x denotes the number of possible zeros. In this case, the largest exponent of x is 1. So there is only ONE zero for f(x) = - 4x + 6.

And now we need to factor the function. As this is a simple function, it cannot be further factored.

Now, each part of the function is to be set to zero to find out the zero of the function.

So, -4x + 6 = 0

      -4x = -6

         x = -6/-4

         x = 1.5

So, the function f(x) = - 4x + 6 has only one zero which lies at

x = 1.5

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