SOLUTION: Find the discontinuiny, and the zeros of the function for f(x) = the quantity negative x squared plus x plus 20 over the quantity x plus 4 (-x^2+x+20/x+4)

Question 980068: Find the discontinuiny, and the zeros of the function for f(x) = the quantity negative x squared plus x plus 20 over the quantity x plus 4 (-x^2+x+20/x+4)
Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
To find the discontinuity of the function we will look at the denominator and determine what value for x will result in the denominator equalling 0, since the denominator cannot equal 0. To do this, we will set our denominator equal to 0:

x + 4 = 0

Subtract 4 from both sides, giving us:

x = -4

Therefore, our discontinuity is x = -4

To find our zeroes, we will set our function equal to 0:

Next, multiply both sides of the equation by (x + 4) to rid ourselves of our fraction on the left side of the equal sign. This will result in:

Third, multiply the entire equation by -1 to make the equation easier to factor. This will give us:

Fourth, factor the left side of the equation. This will result in:

Set each set of parentheses equal to zero and solve for x:

----->

----->

Since we have determined that -4 is NOT a zero since it will result in a zero value in our denominator, our only zero is

We can verify by substituting the x in our original equation with 5:

-----> -----> -----> .

Since is a true statement, 5 is, in fact, the zero of our function.
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