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If L+M+N=0 and L,M,N are rationals the r...

If `L+M+N=0 and L,M,N` are rationals the roots of the equation `(M+N-L)x^2+(N+L-M)x+(L+M-N) = 0` are

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Knowledge Check

  • IF l,m,n are rational the roots of (m +n) x^2 -(l+m+n)x+l =0 are

    A
    rational
    B
    rational and equal
    C
    rational and not equal
    D
    irrational

  • Givne lines are (x-1)/(l) = (y + 1)/(m) = z/n and (x+1)/(m) = (y-3)/(n) = (z-1)/(l) where l gt m gt n l,m, n are roots of the equation x^3 + x^2 -4 x = 4 then the angle between them is ........

    A
    `pi/2`
    B
    `cos^(-1)(1/4)`
    C
    `cos^(-1)(-4/9)`
    D
    `cos^(-1)(5/9)`

  • If l,m,n are direction cosines of the line then -l,-m,-n can be

    A
    only direction ratios of the line
    B
    only direction cosines of the line
    C
    direction cosines and direction ratios of the line
    D
    neither direction cosines nor direction ratios of the line

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    the acute angle between two lines such that the direction cosines l, m, n of each of them satisfy the equations l + m + n = 0 and l^2 + m^2 - n^2 = 0 is

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    The acute angle between two lines such that the direction cosines l, m, n, of each of them satisfy the equations l + m + n= 0 and l^2 + m^2 – n^2 = 0 is:

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