Find all zeros 5x^5-20x^4-40x^3-16x^2-45x+180=0

- anonymous

Find all zeros 5x^5-20x^4-40x^3-16x^2-45x+180=0

- jamiebookeater

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- anonymous

@zepp

- anonymous

What do you mean by "Find all zeros" ?

- anonymous

find the zeros of th eq

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## More answers

- anonymous

Use rational root theorem to find first zero. Then use synthetic division to factor it out.

- anonymous

hi @evy15 are you in numerical analysis?
the root are -2.07316, 1.2355, 5.5573 and two complex roots
check it for yourself if they are true

- anonymous

@evy
though the equation is 5x^5-20x^4-40x^3-16x^2-45x+180=0 correct
bu t may be i feel u have typed in -16X^2 instead of 160x^2

- anonymous

no its correct

- anonymous

can someone please help me and explain to me how to begin this problem

- anonymous

can someone respond

- mathmate

Have you done numerical methods in your course?
This is not a problem that can be solved by factorization, or rearrangements.
I suggest you triple check the question.

- anonymous

its correct can you tell me how to begin

- mathmate

It can be solved numerically, or graphically. Are these expected methods to use in your course?

- anonymous

yes the thing is i missed a day in class and now i dont know how to work this out

- mathmate

Are you working on factorization, Descartes rule of signs, etc.?
I suggest you check your course outline to see what you're expected to know, or check with a friend to see what has been done that day. The prof would also be pleased to tell you what has been covered that day.
This problem requires numerical methods which are techniques completely different from your previous problems.

- anonymous

can u help me and explain it to me

- anonymous

i have tried to use the book but i keep getting it wrong

- mathmate

What is the name of your math course?

- anonymous

Algebra 2

- mathmate

Then there is probably another typo in the question.

- anonymous

there isn't, i already checked

- mathmate

I believe you, but your prof made a typo!
Check in the index of your textbook to see if Newton's method is in there.
What is the title of your textbook?

- anonymous

ok

- anonymous

Im not sure, hold on

- anonymous

Holt McDougal Larson Algebra 2

- mathmate

Can you find "Newton's method" in the index?

- mathmate

On which chapter are you working?

- mathmate

Is it paper home-work or online?

- anonymous

its a take home test and i couldnt find it

- mathmate

As matricked pointed out, IF -16x^2 had been +160x^2, then there are rational roots obtainable by grouping.
5x^5-20x^4-40x^3+160x^2-45x+180
=5(x^5-4x^4-8x^3+32x^2-9x+36)
\(= 5( x^4(x-4) -8x^2(x-4) -9(x-4)) \)
\(= 5(x-4)(x^4-8x^2-9) \)
\(= 5(x-4)(x^2-9)(x^2+1) \)
\(= 5(x-4)(x+3)(x-3)(x^+1) \)

- mathmate

*last factor is \( (x^2+1) \)

- anonymous

ok do you solve for them now

- anonymous

hold on a second, im sorry

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