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Math Help - quadradic equation condition

  1. #1
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    Smile quadradic equation condition

    Please help!!

    x^2+2px+(3p+4)=0 , where p is a positive constant, has equal roots

    a) Find the value of p.

    b) for this value of p, solve the equation.
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  2. #2
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    Greetings,

    First of all, think when quadratic equations have equal roots.
    From there you get two values for p, one of which is negative and solving the equation with the other p is not a problem, I shall assume.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by randomised View Post
    Please help!!

    x^2+2px+(3p+4)=0 , where p is a positive constant, has equal roots

    a) Find the value of p.

    b) for this value of p, solve the equation.
    An equation has repeating [equal] roots when the discriminant is equal to zero.

    \Delta=b^2-4ac\implies \Delta=(2p)^2-4(1)(3p+4)=4p^2-12p-16

    Thus, \Delta=0 when 4p^2-12p-16=0\implies p^2-3p-4=0

    Can you take it from here and solve for p?

    --Chris
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by randomised View Post
    Please help!!

    x^2+2px+(3p+4)=0 , where p is a positive constant, has equal roots

    a) Find the value of p.

    b) for this value of p, solve the equation.
    Set the discriminant to zero for a double root.


    b^2-4ac=0

    a = 1

    b = 2p

    c = 3p + 4
    Geeze! Way too slow today!
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  5. #5
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    Perhaps D = k^2 - ac, k = b/2 would shorten the path.
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