alg2/trig

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If 4x^2+9=kx, what value of k will produce equal roots?

the answer is 12 but i don't understand how you get it, please help!

  • alg2/trig -

    4 x ^ 2 + 9 = kx

    4 x ^ 2 - k x + 9 = 0

    Quadratic equation has two real roots, if Discrininant Ä = 0

    Ä = b ^ 2 - 4 * a * c

    In this case :

    a = 4

    b = - k

    c = 9


    Ä = b ^ 2 - 4 * a * c


    Ä = ( - k ) ^ 2 - 4 * ( 4 ) * 9

    Ä = k ^ 2 - 144 = 0

    k ^ 2 - 144 = 0

    k ^ 2 = 144

    k = sqrt ( 144 )

    k = ± 12


    For k = - 12

    4 x ^ 2 + 9 = k x

    not equal becouse left side of equation are positive ( 4 x ^ 2 + 9 ) are allways great of 0 ) ,and right side of equation are negative.

    So solution are k = 12

  • alg2/trig -

    Quadratic equation has two real equals roots, if Discrininant Ä = 0

    Ä = greek letter Delta

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