Would the zeros of the equation 2x^4-5x^3-3x^2=0 be -2,5,-3?

Question

barrycarter · Answer

What about 0 itself?

anonymous · Answer

Would that be in with the zeros of the function?

barrycarter · Answer

What you have is actually an equation, but when x=0, what does the function become? Also, it should have only 2 other 0's, not 3.

anonymous · Answer

okay so its and equation... I dont quite understand how to do this. It says to solve on calculator and find the zeros... I tried and only got -2,5, and 3.

jim_thompson5910 · Answer

how did you get -2 and 5?

anonymous · Answer

Laughs/... I honestly do not know :/

barrycarter · Answer

Are you studying algebra or pre-algebra?

anonymous · Answer

Algebra II

jim_thompson5910 · Answer

2x^4-5x^3-3x^2=0 

x^2(2x^2 - 5x - 3) = 0

x^2(2x^2 - 6x + x - 3) = 0

x^2(2x(x - 3) + 1(x - 3)) = 0

x^2(2x + 1)(x - 3) = 0

Can you take it from here?

anonymous · Answer

May you explain what you are doing? Pleease?

jim_thompson5910 · Answer

Sure thing

In step 2, I'm factoring out the GCF x^2

Then I broke up -5x into -6x + x. This is because -6 and 1 multiply to -6 and add to -5 (notice how 2 times -3 = -6)

From there, I'm factoring by grouping

jim_thompson5910 · Answer

Does that clear things up?

anonymous · Answer

Oh okay i get that now...

jim_thompson5910 · Answer

alright, tell me what you get for the answer

anonymous · Answer

So after that last part What would i do i am so so sorry lol

jim_thompson5910 · Answer

it's ok

jim_thompson5910 · Answer

use the zero product property

x^2(2x + 1)(x - 3) = 0

x^2 = 0 or 2x + 1 = 0 or x - 3 = 0

x = 0 or 2x = -1 or x = 3

x = 0 or x = -1/2 or x = 3


Keep in mind that the x^2 = 0 means that you'll have the root x = 0 with a multiplicity of 2

anonymous · Answer

I just need explantation i get confused easy

jim_thompson5910 · Answer

Let me know if that makes sense or not

anonymous · Answer

Okay so... the GCF is x^2 and you would factor the whole thing by regrouping... got that so far... then you would find the zeros with, the zero product property okay after find the ones that equal to zero and those are your answers?

jim_thompson5910 · Answer

yes the term 'zeros' are a bit confusing, so you can call them roots or solutions

so when they say "find the zeros", they mean "find the roots or solutions"

The roots/solutions in this case are:  x = 0, x = -1/2,  or x = 3

anonymous · Answer

Oh Okay i see i get it now i always wonder about roots vs. zeros.... Understanding now thank you!

jim_thompson5910 · Answer

that's great

anonymous · Answer

Your the best... (:

jim_thompson5910 · Answer

thanks for thinking so, always glad to help

anonymous · Answer

Your welcome :) <3