anonymous
  • anonymous
List all the real and imaginary zeros of f(x) = x^3+x^2+ 13x - 15... 1 is a zero of the function
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
did you factor? you already knew 1 was a zero, from the last question
Callisto
  • Callisto
I think the question asks to solve f(x) =0 Since the question gives you 1 is a zero of the function. (x-1) is a factor. Now, do the division to get the other factor first, can you?
anonymous
  • anonymous
once you factor, you find the other zeros using the quadratic formula

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anonymous
  • anonymous
You said (x−1)(x^2+2x+15) This gives zeros of 1, 3, 5, 15?
Callisto
  • Callisto
Nope!~ f(x) =0 x^3+x^2+ 13x - 15 =0 (x−1)(x^2+2x+15) =0 So, x-1 =0 -(1) or (x^2+2x+15) =0 -(2) You can solve (1) easily. And solve (2) using quadratic formula!~
Callisto
  • Callisto
For a quadratic equation ax^2 + bx + c=0 \[x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]^ Quadratic formula
anonymous
  • anonymous
i get \[(-4\sqrt{15}) /2\]
Callisto
  • Callisto
It doesn't seems right... \[x=\frac{-2 \pm \sqrt{2^2 - 4(1)(15)}}{2(1)} =?\]
anonymous
  • anonymous
-2i√14?
Callisto
  • Callisto
Nope.. \[x=\frac{-2\pm \sqrt {-56}}{2} = \frac{-2\pm -2\sqrt {-14}}{2} = -1 \pm -14i\]
anonymous
  • anonymous
\[\sqrt{14}i\]
anonymous
  • anonymous
a typo
Callisto
  • Callisto
Sorry :S \[-1\pm -\sqrt{14}i\]
anonymous
  • anonymous
Im still not sure how I get the real and imaginary zeros off that...
Callisto
  • Callisto
the real one is 1 the imaginary ones are \[-1\pm -\sqrt{14}i\] Actually, the question just asks to you to solve f(x) =0 ... I think..
anonymous
  • anonymous
Thankssss!
Callisto
  • Callisto
Welcome!!~~~

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