find the zeroes of f(x) = 7 + 8x - x^2.

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My homework problem says find the zeroes of \(\displaystyle f(x) = 7 + 8x - x^2\).

So I tried the rational roots theorem and got plus/minus 1 and plus/minus 7.

None of those roots worked for me. I don't know what I am doing wrong. Can someone please help me?


Thank you.
 
Perhaps you should try again. How did you calculate the value to see if it was zero? Did you notice the function is listed in INcreasing order of the exponent? It will not help if it is backwards.
 
tkhunny said:
Perhaps you should try again. How did you calculate the value to see if it was zero? Did you notice the function is listed in INcreasing order of the exponent? It will not help if it is backwards.
Click to expand...

I used synthetic division. I did notice the function is listed in increasing order, so when I divided, my numbers were -1, 8, and 7.

My possible roots were plus/minus 1 and plus/minus 7

The last number I got when using synthetic division for each possible root were:

1 = 14
-1 = -2
7 = 14
-7 = -98


So none of them were zero.

Do you think this is a simple calculation error on my part?
 
So....there are no rational roots. That happens!

f(x) = -x^2 + 8x + 7

Did it occur to you that you could use the quadratic formula? That will give you the roots regardless of whether they are rational or not (and even if they are complex!).
 
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