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19 November, 13:19

The function f is defined by f (x) = x^2+3x-10 If f (x+5) = x^2+kx+30, k = Find the smallest zero of f (x+5), x=

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  1. 19 November, 13:39
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    F (x+5)

    just replace all x's with x+5 in first equation

    f (x+5) = (x+5) ^2+3 (x+5) - 10

    f (x+5) = x^2+10x+25+3x+15-10

    f (x+5) = x^2+13x+30

    compare

    f (x) = x^2+3x-10

    f (x+5) = x^2+13x+30

    now we can set it to zero

    f (x+5) = 0

    0=x^2+13x+30

    factor

    0 = (x+3) (x+10)

    set each to zero

    x+3=0

    x=-3

    x+10=0

    x=-10

    -10<-3

    smalles zero is x=-10
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