Question

8. 2/6 points I Previous Answers SwokATG13 4.3.018 Find the zeros of f(x), and state the multiplicity of each zero. (Order your answers from smallest to largest x.) fx) x(x 4)(2x 7) X with multiplicity 1 with multiplicity 3 x = 1-4 with multiplicity 2 Need Help? Read ItWatchtTalk to a Tutor Submit Answer Save Progress Practice Another Version -4 points SwokATG13 4.3,019 O Type here to search O e 99+

Answer 1

Solution:

$\small f\left ( x \right )=x\left ( x+4 \right )^{3}\left ( 2x-7 \right )^{2}$

Put   $\small f\left ( x \right )=0$

$\small \therefore x\left ( x+4 \right )^{3}\left ( 2x-7 \right )^{2}=0$

$\small \therefore x=0$

$\small \left ( x+4 \right )^{3}=0\Rightarrow x=-4\: \: \: \left ( thrice \right )$

$\small \left ( 2x-7 \right )^{2}=0\Rightarrow x=\frac{7}{2},\frac{7}{2}$

$\small {\color{DarkRed} x=-4}$  with multiplicity $\small {\color{DarkRed} 3}$

$\small {\color{Magenta} x=0}$   with multiplicity $\small {\color{Magenta} 1}$

$\small {\color{DarkGreen} x=\frac{7}{2}}$ with multiplicity $\small {\color{DarkGreen} 2}$