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Math Help - Roots of the Equation

  1. #1
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    Roots of the Equation

    The roots of the equation
    ax^2 + 4x = 2 are real, rational, and equal when a has a value of

    (1) 1 (3) 3
    (2) 2 (4) 4


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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    The roots of the equation
    ax^2 + 4x = 2 are real, rational, and equal when a has a value of

    (1) 1 (3) 3
    (2) 2 (4) 4


    If a=1, then x^2+4x+2=0 has irrational roots. (Use quadratic formula)

    If a=2, then 2x^2+4x+2=0. Dividing all terms by 2, we have:

    x^2+2x+1=0. Now factor to get:

    (x+1)(x+1)=0. We have 2 equal roots (double root) at x=-1

    If you test a=3 and a-4, you'll see that they have imaginary roots.
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  3. #3
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    ok...........

    Quote Originally Posted by masters View Post
    If a=1, then x^2+4x+2=0 has irrational roots. (Use quadratic formula)

    If a=2, then 2x^2+4x+2=0. Dividing all terms by 2, we have:

    x^2+2x+1=0. Now factor to get:

    (x+1)(x+1)=0. We have 2 equal roots (double root) at x=-1

    If you test a=3 and a-4, you'll see that they have imaginary roots.
    A wonderful repy as always.
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