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If a ne b ne c, "prove that" (a, a^(2)),...

If `a ne b ne c, "prove that" (a, a^(2)), (b, b^(2)), (0, 0)` will not be collinear.

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If alpha , beta are the roots of ax^(2) +bx+c=0, ( a ne 0) and alpha + delta , beta + delta are the roots of Ax^(2) +Bx+C=0,(A ne 0) for some constant delta , then prove that (b^(2)-4ac)/(a^(2))=(B^(2)-4AC)/(A^(2)) .

Prove that the points A(a, 0), B(0, b) and C(1, 1) are collinear, if (1)/(a) + (1)/(b) = 1.

Knowledge Check

  • If the points A(1,2) , B(0,0) and C (a,b) are collinear , then

    A
    a=b
    B
    a=2b
    C
    2a=b
    D
    a=-b

  • If a xx b = c xx b ne 0 , then

    A
    `a = lambdab`
    B
    `a-b=lambdac`
    C
    `(a-c) = lambdab`
    D
    none

  • If a,b, are three non-zero real numbers such that a + b + c =0, and b ^(2) ne ca, then the value of (a ^(2) + b ^(2) + c ^(2))/( b ^(2) - ca ) is

    A
    3
    B
    2
    C
    0
    D
    1

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    Let a,b,c in R and a ne 0 be such that (a + c)^(2) lt b^(2) ,then the quadratic equation ax^(2) + bx +c =0 has

    If a + b + c ne 0 and |(a-x,c,b),(c,b-x,a),(b,a,c-x)| = 0 then total number of different values of x is equal to

    {:(" Column I ( Crystal system)", "( Column II (Axial ratio)"),("(A) Tetragonal", "(p)" a ne b ne c"," alpha = beta = gamma = 90^(@)),("(B) Rhombic" , "(q)" a = b ne c"," alpha = beta = gamma = 90^(@)),("(C)Monoclinic" , "(r)" a ne b ne c"," alpha ne beta ne gamma ne 90^(@)),("(D) Triclinic" , "(s)" a ne b ne c"," alpha = gamma = 90^(@) ne beta):}

    If a+ (1)/(b) = b + (1)/(c) = c + (1)/(a) , where a ne b ne c ne0, then the value of a ^(2) b ^(2) c ^(2) is .

    If a + b = 2c, then the value (a)/(a -c) + (c)/( b -c) is equal to (where a ne b ne c )

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