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Match the following for the equation x^(...

Match the following for the equation `x^(2)+a|x|+1=0` where, a is a parameter.

Text Solution

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The correct Answer is:
`a to s; b to r; c to q; d to p `
`atos,btor,ctoq,d""to""p`
Obviously when `age0`, we have no roots a all the terms are followed by+ve sign. Also for a=-2, we have
`x^(2)-2|x|+1=0`
or `|x|-1=0impliesx=pm1`
Hence, the equation has two roots. Also when `alt-2`, for given equation
`|x|=(-apmsqrt(a^(2)-4))/(2)gt0`
Hence, the equation has four roots as `|-a|gtsqrt(a^(2)-4)`. Obviously, the equation has no three roots for any value of a.
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Knowledge Check

  • If the roots of the equation x^(2)+px+c=0 are 2,-2 and the roots of the equation x^(2)+bx+q=0 are -1,-2, then the roots of the equation x^(2)+bx+c=0 are

    A
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    B
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    C
    `1,-4`
    D
    `-5,1`

  • The value of discriminant of the equation x^(2)+x+1=0 is …………

    A
    -4
    B
    -3
    C
    3
    D
    4

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