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Math Help - simultaneous equations and uadratic inequalities

  1. #1
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    Question simultaneous equations and uadratic inequalities

    1. find the values of k such that y=2x+k is a tangent to the curve with equation y=xsquared+1
    answer=0



    2. find the values of k such that y=kx-2 is a tangent to the curve with equation y=xsquared+1
    answer=plus minus 2squareroot3

    please respond quickly
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  2. #2
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    Hello, wale!

    2. Find the values of k such that y\:=\:kx-2
    is a tangent to the curve with equation y\:=\:x^2+1

    If the line is tangent to the parabola, they intersect at exactly one point.

    Intersections: . x^2+1 \:=\:kx-2 \quad\Rightarrow\quad x^2 - kx + 3 \:=\:0

    Quadratic Formula: . x \;=\;\frac{k \pm \sqrt{k^2-12}}{2}


    If the quadratic equation has one root, the discriminant must be zero:

    . . k^2-12 \:=\:0 \quad\Rightarrow\quad k^2 \:=\:12 \quad\Rightarrow\quad k \:=\:\pm\sqrt{12} \:=\:\pm2\sqrt{3}

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  3. #3
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    Quote Originally Posted by wale View Post
    please respond quickly
    Respond to what? I see no question.
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