Question

id="TexFormula1" title="f(x) = {x}^{3 } + {3x}^{2} - 9x + 5" alt="f(x) = {x}^{3 } + {3x}^{2} - 9x + 5" align="absmiddle" class="latex-formula">
which of the following are roots of a polynomial function?
check all that apply
a$1 - \sqrt{3}$
b
$1 + \sqrt{3}$
c
$- 5$
D
$3 - \sqrt{2}$
E
$3 + \sqrt{2}$
F
$1$
​

Answer 1

Answer:

$f(1) = {(1)}^{3} + 3 {(1)}^{2} - 9(1) + 5 \\ (x - 1) = 0 \rightarrow \: x = 1 \\\frac{{x}^{3 } + {3x}^{2} - 9x + 5}{x - 1} = {x}^{2} + 4x - 5 \\ (x + 5)(x - 1) = 0 \\ x = - 5 \: or \: x = 1 \\ \color{red}\boxed{x_{1} = 1} \\\color{yellow} \boxed {x_{2} = 1} \\ \color{green}\boxed{x_{3} = - 5}$

The answer would be C and F