anonymous
  • anonymous
Part 1 [3 points]: What are the possible number of positive, negative, and complex zeros of f(x) = –2x3 – 5x2 + 6x + 4 ? Part 2 [4 points]: Use complete sentences to explain the method used to solve this equation.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
This is algebra 2
anonymous
  • anonymous
Medal For the answer
Luigi0210
  • Luigi0210
I got you. Let's set it up for synthetic division

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anonymous
  • anonymous
ok ty
Luigi0210
  • Luigi0210
|dw:1370548522537:dw| Try this
anonymous
  • anonymous
huh? Why is it 2?
Luigi0210
  • Luigi0210
have you not learned synthetic division yet?
anonymous
  • anonymous
i have but forgot how it works
anonymous
  • anonymous
can u just answer it? plz This is the last essay on my exam
Luigi0210
  • Luigi0210
|dw:1370548850771:dw| I can't give answers
anonymous
  • anonymous
ok what now?
anonymous
  • anonymous
its -2x^3-4x^2+8x-0?
Luigi0210
  • Luigi0210
Uhm, no..
anonymous
  • anonymous
-2x^2-4x+8?
Luigi0210
  • Luigi0210
There you go, now to find the remaining solutions, you have to factor out a -2, and then use the quadratic formula
anonymous
  • anonymous
explain plz :)
anonymous
  • anonymous
anyone know the answer?
Luigi0210
  • Luigi0210
So from using synthetic division we are left with this: \[(2x+1)(-2x^2-4x+8)\] right? Now we have to factor out a -2 to make it easier: \[(2x+1)(-2)(x^2+2x-4)\] since we can't factor this we have to use the quad formula:
Luigi0210
  • Luigi0210
And if you want someone else to help then fine, I suppose I can just leave
campbell_st
  • campbell_st
well the answer to part 1 is 3... since the highest power of the equation is 3. The power is equal to the number of zeros or root. For part 2... its there is a test called the rational roots test, take the factors of the constant 4(q) and divide them by the factors of the coefficient of the leading term -2 (P) and so the rational roots will be (q)/(p) this appears to have been what @Luigi0210 has done to come up with a factor of -1/2. Not an obvious choice. he has then done a synthetic division to should the quadratic factor so that \[-2x^3 - 5x^2 + 6x + 4 = (x + \frac{1}{2})(-2x^2 - 4x +8)\] but it could be written more correctly as \[(2x + 1)(-x^2 - 2x + 4)\] all you need to do is use the general quadratic formula on \[-x^2 -2x + 4 = 0\] to find the other roots, which will be irrational. hope this makes sense
campbell_st
  • campbell_st
@Luigi0210 based on your factorisation, the leading term has a coefficient of -4
anonymous
  • anonymous
ok?
anonymous
  • anonymous
ill se what i can make of it
anonymous
  • anonymous
can u help plz
anonymous
  • anonymous
i cant formulate it into an essay
anonymous
  • anonymous
@campbell_st plz
campbell_st
  • campbell_st
ok... so part 1... the function f(x) will have 3 roots. This is because the leading term is \[-2x^3 \] and has a power of 3. The number of roots is equal to the highest power in f(x) Part(2) the rational root theorem says that let the factors of the constant 4 be q \[q = \pm1, \pm2, \pm4\] let the factors of the leading -2 be p \[p = \pm1, \pm2\] the theorem says a rational root will be q/p so to find a root you need to substitute the different values of q/p into f(x) until you ger f(q/p) = 0 then you have a root. this is how @luigi0210 came up with -1/2 as a root next step is polynomial division or synthetic division to find other factors. using @luigi0210 division above the factors are \[-2x^3 - 5x^2 + 6x + 4 = (2x + 1)(-x^2 -2x + 4)\] so you have (2x + 1) gives the root, x = -1/2 so you need the general quadratic formula \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\] with the expression \[-x^2 -2x + 4\] so to use the formula a = -1, b = -2 and c = 4 which when substituted will give the roots of \[x = -1 \pm \sqrt{5}\] when simplified. hope this makes sense, and covers the 2nd part of the question.
Luigi0210
  • Luigi0210
thank you @campbell_st

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