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ab x^2+(b^2-a c)x-b c=0...

`ab x^2+(b^2-a c)x-b c=0`

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If the roots of the quadratic equation (a-b) x^(2) + (b - c) x + (c - a) =0 are equal , prove that b +c = 2a

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Knowledge Check

  • If a,b,c are in A.P. and if the equations (b - c) x^(2) + (c - a) x + (a - b) = 0" " (1) and 2(c +a) x^(2) + (b+ c) x = 0" " (2) have a common root, then

    A
    `a^(2), b^(2), c^(2)` are in A.P.
    B
    `a^(2), c^(2), b^(2)` are in A.P.
    C
    `c^(2), a^(2), b^(2)` are in A.P.
    D
    none of these

  • The equation (b-c) x^(2)+ (c-a) x+(a-b)=0 has

    A
    equal roots
    B
    irrational roots
    C
    rational roots
    D
    none of these

  • x^(2) +(a+b+c)x+ab +bc = _______

    A
    `(x+a)(x+b+c)`
    B
    `(x+c)(x+a+b)`
    C
    `(x+b)(x+a+c)`
    D
    `(x+a)(x+b-c)`

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    a,b and c are non-zero distinct real numbers, common root of equations (a-b)x^(2)+(b-c)x+(c-a)=0c(a-b)x^(2)+a(b-c)x+b(c-a)=0 is

    Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

    If roots of equation a-b)x^(2)+(b-c)x+(c-a)=0 are equal then prove that b+c=2a

    If a,b and c are in AP and if the equations (b-c)x^(2)+(c-a)x+(a-b)=0 and 2(c+a)x^(2)+(b+c)x+(a-b)=0 have a common root,then

    If (a-b)x^(2)+2(b-c)x+(a-c+b)=0 (a,b,c in R) and x^(2)+2x+5=0 have a common root,value of a,b and c

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