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Let α and β be the roots of 3x2+4x+9=0. Then (1+α)(1+β) can be expressed in the form ab, where a and b are coprime positive integers. Find a+b.

  • math -

    since the roots are
    -2/3 ±√23/3 i

    1+α = 1/3 + √23/3 i
    1+β = 1/3 - √23/3 i

    (1+α)(1+β) = 1/9 + 23/9 = 24/9 = 8/3

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