Find the zeros of the polynomial function and state the multiplicity of each.

f(x) = 3(x + 8)2(x - 8)3

Question

Find the zeros of the polynomial function and state the multiplicity of each.

f(x) = 3(x + 8)2(x - 8)3

lovelyharmonics · Answer

@surjithayer ._. im sorry to keep bothering you

anonymous · Answer

Refer to the attached plot.

lovelyharmonics · Answer

what is that? o.O

anonymous · Answer

put x+8=0,x=-8 isa zero of multiplicity 2
x-8=0,x=8 is a zero of multiplicity 3

lovelyharmonics · Answer

okay but what about the 3 out in front?

lovelyharmonics · Answer

if you could, i have a few other questions that i need help with too c:

anonymous · Answer

The attachement is a plot of$$x^5-8 x^4-128 x^3+1024 x^2+4096 x-32768 $$

lovelyharmonics · Answer

Find a cubic function with the given zeros.

Square root of seven., -Square root of seven., -4

how are you so good at math?(◕︵◕)

anonymous · Answer

$$f(x)=\left( x-\sqrt{7} \right)\left( x+\sqrt{7} \right)\left( x+4 \right)=?$$
solve first two first

lovelyharmonics · Answer

theyd be the opposite so -sqrt7 would be sqrt7 and sqrt7 would be -sqrt7

anonymous · Answer

$$x=\sqrt{7} ~is`~a ~zero~of~f(x)~so~x-\sqrt{7}~is ~a~factor~of~f(x)$$

lovelyharmonics · Answer

wait what? 0.o

anonymous · Answer

This is the reason for changing sign

lovelyharmonics · Answer

changing the sign? didnt you just subtract sqrt7 from both sides?

anonymous · Answer

$$\left( a+b \right)\left( a-b \right)=a^2-b^2$$
x^2+2x-3=(x+3)(x-1)
it has zeros -3 and 1 
but x+3 and x-1 are factors

anonymous · Answer

$$\left( x+\sqrt{7} \right)\left( x-\sqrt{7} \right)=x^2-(\sqrt{7})^2=x^2-7$$

lovelyharmonics · Answer

okay, but i was right? so -sqrt7 and sqrt7 are 2 of the answers

anonymous · Answer

correct ,they are zeros.

lovelyharmonics · Answer

yay c: okay so what about the tricky last part?

lovelyharmonics · Answer

wait isnt it just -4?

anonymous · Answer

solve$$\left( x^2-7 \right)\left( x+4 \right)$$

anonymous · Answer

solve means multiply.

lovelyharmonics · Answer

x^3+4x^2-7x-28

anonymous · Answer

correct

lovelyharmonics · Answer

okay one more question c: State the domain of the rational function.
f(x) = seven divided by quantity fourteen minus x.

anonymous · Answer

$$f(x)=\frac{ 7 }{14-x }$$
it is defined for all values except where  denominator is 0
for domain$$14-x \neq 0~ or~x \neq14$$
domain is all real values except x=14

lovelyharmonics · Answer

its that easy? o.o

anonymous · Answer

yes

lovelyharmonics · Answer

okay thank you c:

anonymous · Answer

yw