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christinewilliams
 3 years ago
Identify the roots of 3x^321x^2+72x+540=0State the multiplicity of each root.
christinewilliams
 3 years ago
Identify the roots of 3x^321x^2+72x+540=0State the multiplicity of each root.

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christinewilliams
 3 years ago
Best ResponseYou've already chosen the best response.0The root 5 has a multiplicity of 1, and the root 6 has a multiplicity of 2. The root 5 has a multiplicity of 1, and the root 6 has a multiplicity of 2. it could be either one of those and i dont know which one it is i think it is the first one

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.06 is not a root, if you put it in the equation, you do not get 0. 6 is a root, as is 5. Start with 5 as a root, you then know that you could write the eq. as\[(x5)(2nd \deg polynomial)\]You could find out about the 2nd degree polynomial by doing a long division, or a synthetic division, which is very fast. It gives:\[(x5)(3x^236x108)=0\]Factoring out a 3 helps to find the other (double) solution 6. If you need help with long division or synthetic division, just yell ;)

Shashank_
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1354857604034:dw

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.0The last step:\[(x5)(3x^236x108)=0\]Factor out 3:\[3(x5)(x^212x36)=0\]Factorize the 2nd degree part:\[3(x5)(x6)^2=0\]Now you can see that 5 is a single root and 6 a double one.
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