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Quadratic and cubic equation -show that -(common roots)

  1. Aug 20, 2011 #1
    1. The problem statement, all variables and given/known data

    If the equations ax2+bx+c=0 and x3+3x2+3x+2=0 have two common solutions then show a=b=c.

    2. Relevant equations



    3. The attempt at a solution

    first equation will be the factor of second.
    taking out common from first equation.


    how to show a=b=c??
    please provide hints.
     
  2. jcsd
  3. Aug 20, 2011 #2

    SammyS

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    Find a real root of the cubic equation. Write the cubic polynomial as the product of a quadratic factor and a linear factor.
     
  4. Aug 20, 2011 #3

    PeterO

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    factorise the cubic.
     
  5. Aug 20, 2011 #4

    uart

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    The easiest way to approach this is to divide (x^3 + 3x^2+ 3x + 2) by (x^2 + x +1) to prove that it's a factor. You don't actually need to factorize, just verify that the factor.
     
  6. Aug 20, 2011 #5
    can we solve by the following formulas

    for quadratic eqs.
    α+ß =-b/a

    αß= c/a

    for cubic equations
    (Γ=gamma)

    α+ß+Γ=-b/a

    (αß)+(ßΓ)+(αΓ)=c/a

    αßΓ=-d/a



    i am trying to solve by this method but i hung up! in between?
     
  7. Aug 20, 2011 #6
    thank you very much i got it:smile:
     
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