0
$\begingroup$

I am having a hard time understanding this definition.

The definition states.

"If P is a polynomial function, then "c" is called a zero of P if P(c) = 0. In other words, the zeros of P are the solutions of the polynomial equation P(x) = 0. Note that if P(c) = 0, then the graph of P has an x-intercept at x = c, so the x-intercepts of the graph are the zeros of the function.

Real Zeros of Polynomials

If P is a polynomial and c is a real number, then the following are equivalent:

1) c is a zero of P 2) x= c is a solution of the equation P(x) = 0 3) x-c is a factor of P(x) 4) c is an x-intercept of the graph of P."

Been reading this definition for and 1 hour and I just don't get it. Can someone explain it to me as if I am a 5 year old?

$\endgroup$
  • $\begingroup$ The definition of an $x$-intercept of a function $f$ is just a place where $f(x)=0$, so that relates the "intercept" part. Also $x=c$ is a solution of an equation if when you plug that value into the equation it is true (i.e. the equality holds). So that relates the "solution" part. The only non-trivial part is that $x-c$ is a factor of $P$, but without getting too technical, in practice you can check this by performing long division of polynomials $\endgroup$ – user139388 Apr 5 '14 at 21:00
0
$\begingroup$

A number $c \in \mathbb{C}$ (I use $\mathbb{C}$ rather than $\mathbb{R}$ to allow for complex zeroes) is called a zero of a polynomial $P(x)$ if and only if $P(c) = 0$. Graphically, if a number $c$ is a zero of $P(x)$, then the point $(c,0)$ is on the graph of $P$, and so it hits the $x$-axis at the point $c$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.