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Math Help - quadratic problem

  1. #1
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    quadratic problem

    if exactly one root of equation x^2-(k-1)x+k(k+4)=0 lies between the roots of equation x^2-(k+3)x+k+2=0 then value of k=


    i have solved this graphically

    can yu solve this mathematically
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  2. #2
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    Quote Originally Posted by prasum View Post
    if exactly one root of equation x^2-(k-1)x+k(k+4)=0 lies between the roots of equation x^2-(k+3)x+k+2=0 then value of k=


    i have solved this graphically

    can yu solve this mathematically
    1. According to the theorem of Viéte (or do you call him Vieta?) the mean of the 2 solutions of the 2nd equation is \dfrac{k+3}2

    2. Solve the 1rt equation using the quadratic formula. After moving some stuff around you'll get:

    x = \dfrac{(k-1)\pm\sqrt{(k-1)^2-4 \cdot 1 \cdot (k^2+4k)}}2

    3. Using the result from 1. you have to solve for k:

    (k-1)\pm \sqrt{-3k^2-18k+1}= (k+3)

    I'll leave this for you.

    Spoiler:
    I've got k = -1 or k = -5
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  3. #3
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    Quote Originally Posted by earboth View Post
    1. According to the theorem of Viéte (or do you call him Vieta?) the mean of the 2 solutions of the 2nd equation is \dfrac{k+3}2

    2. Solve the 1rt equation using the quadratic formula. After moving some stuff around you'll get:

    x = \dfrac{(k-1)\pm\sqrt{(k-1)^2-4 \cdot 1 \cdot (k^2+4k)}}2

    3. Using the result from 1. you have to solve for k:

    (k-1)\pm \sqrt{-3k^2-18k+1}= (k+3)

    I'll leave this for you.

    Spoiler:
    I've got k = -1 or k = -5
    thanks
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