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Math Help - Year 10 Quadratic inequalities

  1. #1
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    Year 10 Quadratic inequalities

    x^2+4x+13< 0

    Gotta solve the inequation.
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  2. #2
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    Quote Originally Posted by nerdzor View Post
    x^2+4x+13< 0

    Gotta solve the inequation.
    Hello,

    rearrange:

    x^2+4x+13<0~\implies~x^2+4x+4<-13+4~\implies~(x+2)^2<-9

    A square can't never be negative, thus there doesn't exist a real solution.

    If there is a typo and the original inequality reads:

    x^2+4x+3<0~\implies~x^2+4x+4<-3+4~\implies~(x+2)^2<1 then you get:

    -1 < x+2 < 1~\implies~-3 < x < -1
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  3. #3
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    Hello, nerdzor!

    Another approach . . .


    Solve: . x^2 + 4x + 13 \:< \: 0

    We have the function: . y \:=\:x^2 + 4x + 13 . . . a parabola
    . . and they want to know when the graph is below the x-axis.

    Since this is an up-opening parabola, the curve is below the x-axis
    . . in the interval between the x-intercepts.

    The x-intercepts occur when y = 0\!:\;\;x^2 + 4x + 13 \:=\:0
    . . But this equation has no real roots.
    Hence, there are no x-intercepts. .The graph never goes below the x-axis.

    The inequality is never true.

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