• anonymous
Form a polynomial whose zeros and degree are given. Multiply out to form a polynomial. Zeros: 0, -5, 4; degree: 3
  • Stacey Warren - Expert
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  • chestercat
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  • DebbieG
Welcome to Open Study! For a polynomial, each root (or "zero") c corresponds to a factor, x-c. E.g., if I want a polynomial with roots 1 and -1, I can "cook that up" by multiplying the factors associated with each root: \(\Large (x-1)(x-(-1))=(x-1)(x+1)=x^2-1\) So \(\Large x^2-1\) has zeros 1, and -1, because I "cooked it up" that way. :) Now a root of 0 just means a factor of (x-0), or just x. So if I wanted roots of 1, -1, and 0, I need: \(\Large x(x-1)(x+1)=x(x^2-1)=x^3-x\) Now try that with your given roots. :)
  • DebbieG
Just a note to add: if you were asked for the polynomial to have a higher degree with the same roots - say, degree 5 with 3 roots - you would just make some of the roots "repeated" roots. E.g. for my example above, if I wanted degree 5 I could use: \(\Large x^3(x-1)(x+1)\) or \(\Large x^2(x-1)^2(x+1)\) or \(\Large x(x-1)(x+1)^3\) .... you get the idea, just so that the total number of factors is = the required degree.

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