# What is the Positive Root of the Equation? [closed]

Given that: $f(x)=-x^2 - 5x + 2$ and $g(x) = f(x-)$ what is the Positive Root of the equation $f(x) = g(2)$?

This is the Question that my math teacher put on the board, she said if we got the answer in any way, than we would get a prize. I'm not that good at math, and no one I know can solve this question, I would like to know the answer!

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I don't understand what $f(x)$ equals to and I don't understand what does $g(x)=f(x=)$ mean. – Git Gud Feb 25 at 23:44
Also, what is $g(x)$? What does $f(x)-g(2)$ have to do with anything? – user7530 Feb 25 at 23:45
$g(x)=f(x-)$? What does that mean? – Git Gud Feb 25 at 23:49
Maybe you mean $f(x) = x^2 - 5x + 2$, $g(x) = f(-x)$? – TMM Feb 25 at 23:49
@Mycrot99 Read TMM's comment. $f(x)=g(x-)$ doesn't make sense. By the way, do you promise to eat your vegetables if we help you? – Git Gud Feb 25 at 23:53

## closed as not a real question by Jacob Black, Micah, Asaf Karagila, Henry T. Horton, Cameron BuieFeb 26 at 0:23

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.

Assuming the following: $f(x)=-x^2 - 5x + 2$ , $g(x) = f(-x)$

Find $x>0$ such that $f(x) = g(2)$.

$g(2) = f(-2) = -(-2)^2-5(-2)+2 = -4+10+2 = 8$

$f(x)-g(2) = 0$

$-x^2-5x+2-8 = 0$

$-x^2-5x-6 = 0$

$x^2+5x+6 = 0$ (Multiply both sides by -1)

$(x+3)(x+2)=0$

$x=-3,-2$

Those aren't positive roots though the teacher may have meant the 2 and 3 in the second last step possibly.

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Once you're able to figure out what the "$g(x)=f(x-)$" bit is actually supposed to be--I suspect it should be "$g(x)=f(-x)$" or "$g(x)=f(x-a)$" (for some real $a$)--then note that $f(x)=g(2)$ if and only if $f(x)-g(2)=0$. Now note that $f(x)-g(2)$ is a quadratic in $x$. How can you solve such an equation?

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Yes, Tmm is probably right, sorry if im a bit slow on all of this :/ I just dont much know the subject. – Celjiah Feb 25 at 23:56
It's okay. It may simply be that your teacher made a mistake in writing it down, in which case it's hardly your fault that you didn't understand it. Do you know how to solve equations of the form $ax^2+bx+c=0$ for $x$ when $a\neq 0$? – Cameron Buie Feb 25 at 23:58
No, im very sorry :/, The only reason I am really asking is because I might fail math this quarter if I dont get a good bonus :/ , Im honestly as dumb as a doornail when it comes to this stuff.. – Celjiah Feb 26 at 0:00
So you want to pass math by asking the Internet to solve your extra-credit assignment for you? – user7530 Feb 26 at 0:02
The reason for asking the question shouldnt be a concern... right? – Celjiah Feb 26 at 0:06