Xjones
Xjones Xjones
  • 20-06-2017
  • Mathematics
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which of the following represents the zeros of f(x)=x^3-5x^2-3x+15

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irspow
irspow irspow
  • 20-06-2017
"Zeros" are the x-values when f(x)=0

x^3-5x^2-3x+15=0  upon slight rearranging of terms...

x^3-3x-5x^2+15=0  now factor first and second pair of terms

x(x^2-3)-5(x^2-3)=0

(x-5)(x^2-3)=0  and if we factor the second parenthetical term as well

(x-5)(x-√3)(x+√3)=0

So if x=-√3, √3, or 5, f(x)=0

Thus the zeros of f(x) are x={-√3, √3, 5}
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