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A polynomial function function is defined by the equation p(x)=3x3+ax2+bx+7, where a, bE/. If p(-2)=5 and p(1)=14 then the value of a+b is...

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    From p(-2)=5 and p(1)=14
    we have two points (-2,5) and (1,14)

    so,
    3(-8) + a(4) -2b + 7 = 5
    4a - 2b = 22 ----> 2a - b = 11

    3(1) + a(1) + b(1) + 7 = 14 ---> a + b = 4

    adding:
    3a = 15
    a = 5, then b = -1

    a+b = 5-1 = 4

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