anonymous
  • anonymous
The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=−3 Find a possible formula for P(x). I understand what multiplicity is, my question would be is that it says BOTH x=2 and x=0 have a multiplicity of 2, that doesnt make any sense to me.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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misty1212
  • misty1212
HI!!
anonymous
  • anonymous
Hello!
misty1212
  • misty1212
if 0 is a zero with "multiplicity 2" that means one factor is \(x^2\)

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anonymous
  • anonymous
but 2 is also a zero that has a factor of x^2, right?
misty1212
  • misty1212
no
misty1212
  • misty1212
since 2 is a zero, one factor is \(x-2\)
misty1212
  • misty1212
since it is a zero with "multiplicity" 2 there are two of those factors, i.e. \((x-2)^2\)
misty1212
  • misty1212
do you know what "multiplicity " means here?
anonymous
  • anonymous
I believe that multiplicity is the exponent value.
anonymous
  • anonymous
Right? or am i mistaken.
misty1212
  • misty1212
yes that is right
misty1212
  • misty1212
so if \(r\) is a zero with multiplicity \(n\) then one factor is \((x-r)^n\)
anonymous
  • anonymous
Ok, that makes more sense. I don't know why I was so confused. Thank you!

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