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Stuck on Quadratic

  1. Apr 23, 2014 #1

    Atomised

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    1. The problem statement, all variables and given/known data

    Solve 5x^2 - 16tx + 3t^2 for x without using quadratic formula.

    I am interested in understanding the technique - I have the answers already: t/5, 3t

    2. Relevant equations

    I have solved the subsequent question which is:

    tx^2 + (tT - 1)x - T = 0, which seems easier because it breaks into four clusters which can be factored, then refactored and solved. The one I am asking about does not seem amenable to the same approach, or any other that I know.




    3. The attempt at a solution

    I am interested in higher maths but having to mend holes in elementary technique. Thanks in advance.
     
    Last edited: Apr 23, 2014
  2. jcsd
  3. Apr 23, 2014 #2
    is the whole equation 5x^2 - 16tx + 3t^2=0?
     
  4. Apr 23, 2014 #3
    Since 5 and 3 are both prime, you only have 4 different possibilities of how the terms appear when you use the factor method. Perhaps the variable t is throwing you off? Start by letting t = 1 just so it's clearer to you and then go back and solve the equation with t.

    Also, you can only solve for a variable if you have an equation. The original expression must be set equal to 0.
     
  5. Apr 23, 2014 #4

    Atomised

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    Yes - the only other info stated in the question is 'Express x in terms of the other letters'.
     
  6. Apr 23, 2014 #5

    Atomised

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    Ah apologies - I have only stated the LHS, the equation is

    5x^2 - 16tx + 3t^2=0
     
    Last edited: Apr 23, 2014
  7. Apr 23, 2014 #6

    Atomised

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    Thank you Scurty, the t was throwing me.

    (5x - t) (x - 3t)
     
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