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For a alt=0, determine all real roots of...

For a `alt=0,` determine all real roots of the equation `x^2-2a|x-a|-3a^2=0.`

Text Solution

Verified by Experts

The correct Answer is:
`{(1-sqrt2)a,(-1+sqrt6)a}`
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For a a<=0, determine all real roots of the equation x^(2)-2a|x-a|-3a^(2)=0

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Knowledge Check

  • The roots of the expression x^2-2a|x-a|-3a^2=0,alt0 :

    A
    `(1+sqrt2)a,(-1-sqrt6)a`
    B
    `(1-sqrt2)a,(sqrt6-1)a`
    C
    `(1pmsqrt2)a`
    D
    none of these

  • Real roots of the equation x^(2)+5|x|+4=0 are

    A
    `-1,-4`
    B
    1,4
    C
    `-4,4`
    D
    none of these

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