Suppose you know that 3 is one of the zeros of the polynomial p=x^3-x^2-11x+15.
Find all the other zeros.
Briefly explain why you know that you have found all of the zeros.
Hello, gumi!
Suppose you know that 3 is one of the zeros of: $\displaystyle p(x) \:=\:x^3-x^2-11x+15$
Find all the other zeros.
Briefly explain why you know that you have found all of the zeros.
If $\displaystyle x = 3$ is a zero of $\displaystyle p(x)$, then $\displaystyle (x-3)$ is a factor of $\displaystyle p(x).$
We find that: .$\displaystyle p(x) \;=\;(x-3)(x^2+2x-5)$
. . And the other two zeros of $\displaystyle p(x)$ are: .$\displaystyle \boxed{x \:=\:-1 \pm\sqrt{6}}$
A cubic polynomial can have at most three zeros.