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A and B are real numbers such that the two quadratic equations 19x^2+3x+2=0 and Ax^2+Bx+7=0 have a common root. What is the value of A+B

  • Maths -

    19x^2+3x+2=0 has roots
    (-3±√143 i)/38

    since both roots are complex, if the two quadratics share one root, they share both. So,

    Ax^2+BX+7 must be a multiple of 19x^2+3x+2.

    So, it must be 7/2 times, making it

    19(7/2)x^2 + 3(7/2)x + 2(7/2)
    = 66.5x^2 + 10.5x + 7

    A+B = 77

  • Maths -

    thank you very much

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