# Thread: Finding All Real Zeros

1. ## Finding All Real Zeros

It says find all real zeros of the function f(x) = x^5-x^4-7x^3+11x^2-8x+12. I searched all over but everywhere I check is saying to use this theorem thing with the negative signs but our teacher didn't teach us about that, she told us to use a graphing calculator. But I'm confused because the only answers I could find were 2, and -3 but since the highest exponent is 5, shouldn't I have 5 answers?

2. Originally Posted by AnnaLena224
It says find all real zeros of the function f(x) = x^5-x^4-7x^3+11x^2-8x+12. I searched all over but everywhere I check is saying to use this theorem thing with the negative signs but our teacher didn't teach us about that
Was it called the factor theorem?

Originally Posted by AnnaLena224
But I'm confused because the only answers I could find were 2, and -3 but since the highest exponent is 5, shouldn't I have 5 answers?
2 and -3 could be repeated factors.

Have a go at $x^5-x^4-7x^3+11x^2-8x+12 \div (x-2)(x+3)$

Then try to factor the quotient.

3. I factored it and got
x^3-2x^2+x-2
x^2(x-2) 1(x-2)
(x-2)(x^2+1)
x=2
x=i(square root)1

4. Originally Posted by AnnaLena224
I factored it and got
x^3-2x^2+x-2
x^2(x-2) 1(x-2)
(x-2)(x^2+1)
x=2
x=i(square root)1
Therefore your factors are $2,2,-3,i,-i$

5. Originally Posted by pickslides
Was it called the factor theorem?
I think the poster might be talking about Descartes rules of signs in reference to the negative sign comment.