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Prove that equations (q-r)x^2 + (r-p)x +...

Prove that equations `(q-r)x^2 + (r-p)x + p-q = 0` and `(r-p)x^2+(p-q)x+q-r=0` have a common root.

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The roots of the equation (q-r)x^(2)+(r-p)x+(p-q)=0

If the equadratic equation 4x ^(2) -2x -m =0 and 4p (q-r) x ^(2) -2p (r-p) x+r (p-q)-=0 have a common root such that second equation has equal roots then the vlaue of m will be :

Knowledge Check

  • If the equadratic equation 4x ^(2) -2x -m =0 and 4p (q-r) x ^(2) -2p (r-p) x+r (p-q)-=0 have a common root such that second equation has equal roots then the vlaue of m will be :

    A
    0
    B
    1
    C
    2
    D
    3

  • The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

    A
    `(r-p)/(q-r),1`
    B
    `(p-q)/(q-r),1`
    C
    `(p-r)/(q-r),2`
    D
    `(q-r)/(p-q),2`

  • The roots of the equation (q- r) x^(2) + (r - p) x + (p - q)= 0 are

    A
    `(r-p)/(q - r) , (1)/(2)`
    B
    `(p - q)/(q - r) , 1`
    C
    `(q- r)/(p-q) , 1`
    D
    `(r- p)/(p - q) , (1)/(2)`

    • Similar Questions

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    If the equadratic equation 4x ^(2) -2x -m =0 and 4p (q-r) x ^(2) -2p (r-p) x+r (p-q)-=0 have a common root such that second equation has equal roots then the vlaue of m will be :

    If the quadratic equation x^(2)-2x-m=0 and p(q-r)x^(2)-q(r-p)x+r(p-q)=0 have common root such that second equation has equal roots. Then the value of m is

    If the equation x^2 + px + q =0 and x^2 + p' x + q' =0 have common roots, show that it must be equal to (pq' - p'q)/(q-q') or (q-q')/(p'-p) .

    The roots of the equation (q - r) x^(2) + (r - p) x + (p - q) = 0 are :

    The roots of the equation " "(q-r)x^(2)+(r-p)x+(p-q)=0 are :a) (r-p)(q-r), 1 b) (p-q)/(q-r), 1 c) (p-r)/(q-r), 2 d) (q-r)/(p-q), 2

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