anonymous
  • anonymous
Algebraically find the exact real zeros and state the multiplicity of each. f(x) = 32x^3 - 4
Mathematics
chestercat
  • chestercat
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campbell_st
  • campbell_st
well I'd divide by 32 so x^3 - 1/8 1/8 = (1/2)^3 so you are factoring x^3 - (1/2)^3 a^3 - b^3 = (a - b)(a^2 + ab + b^2)
campbell_st
  • campbell_st
let a x and b = 1/2 and substitute
campbell_st
  • campbell_st
so the real zero is x = 1/2 from 1st bracket and 2 brackets (x^2 + 1/2x + 1/4) have unreal roots...

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Directrix
  • Directrix
Click on the link to see the two Complex solutions. http://www.wolframalpha.com/input/?i=0%3D+4x%5E2%2B2x%2B1

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