anonymous
  • anonymous
What is the sum of the roots of the polynomial shown below? F(x)=3x^3+12x^2+3x-18
Mathematics
katieb
  • katieb
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butterflydreamer
  • butterflydreamer
sum of roots = -b/a Note that : F(x) = ax^3 + bx^2 + cx + d
amoodarya
  • amoodarya
try to factor (x-1) because x=1 is one of roots (f(1)=0 if you check)
anonymous
  • anonymous
the sum of the roots are -4

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butterflydreamer
  • butterflydreamer
So you want to find your values of a and b by matching it up :) \[F(x) = ax^3 + bx^2 + cx + d \] \[F(x)= 3x^3 + 12x^2 + 3x - 18\]
butterflydreamer
  • butterflydreamer
you're close :) just missing a negative sign!
butterflydreamer
  • butterflydreamer
If you look at the above, we get: a = 3 b = 12 Sum of roots = \[-b/a\] Therefore sum of roots = -12 / 3 = -4
amoodarya
  • amoodarya
he/she did not miss -
butterflydreamer
  • butterflydreamer
-_- oops, you wrote -4 You're correct! :)
anonymous
  • anonymous
she lol
amoodarya
  • amoodarya
another observation is to write it \[f(x)=3(x-1)(x+3)(x+2)\]

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