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    Find the values of k for which the quadratic equation 9x^2 - kx + (k-7) =0 has one positive and one negative root.
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    (Original post by ming jian)
    Find the values of k for which the quadratic equation 9x^2 - kx + (k-7) =0 has one positive and one negative root.
    Let the 2 roots be x_1 and x_2
    then the equation
    9(x-x_1)(x-x_2)=0
    from this the original equation is
    9x^2-9(x_1+x_2)x+9x_1x_2=0
    so for k
    9x_1x_2=k-7<0
    because one of the root is positive the other is negative
    Another limit for k is that there should be two real roots
    that is
    k^2-36(k-7)>0
    but for k-7<0 this equation is always true.
    From this follows ...... ???
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    agree with ztibor

    in general the product of roots is c/a which in this case is ( k-7 )/9 and this must be negative
 
 
 
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Updated: March 14, 2013
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