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Statement 1 : If (a)/(a(1)),(b)/(b(1)),(...

Statement 1 : If `(a)/(a_(1)),(b)/(b_(1)),( c )/(c_(1))` are in A.P., then `a_(1),b_(1),c_(1)` are in G.P.
because
Statement 2 : If `ax^(2)+bx+c=0` and `a_(1)x^(2)+b_(1)x+c_(1)=0` have a common root and `(a)/(a_(1)),(b)/(b_(1)),( c )/(c_(1))` are in A.P., then `a_(1),b_(1),c_(1)` are in G.P.

A

Statement - 1 is True, Statement - 2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement - 1 is True, Statement - 2 is True, Statement-2 is NOT a correct explanation for Statement-1

C

Statement - 1 is True, Statement - 2 is False

D

Statement - 1 is False, Statement - 2 is True

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • If the two equations a a_(1)x^(2)+b_(1)x +c_(1)=0 and a_(2)x^(2)+b_(2)x+c_(2)=0 have a common root, then the value of (a_(1)b_(2)-a_(2)b_(1)) (b_(1)c_(2)-b_(2)c_(1)) is

    A
    `-(a_(1)c_(2)-a_(2)c_(1))^(2)`
    B
    `(a_(1)a_(2)-c_(1)c_(2))^(2)`
    C
    `(a_(1)c_(1)-a_(2)c_(2))^(2)`
    D
    `(a_(1)c_(2)-a_(2)c_(1))^(2)`

  • If two equation a_(1) x^(2) + b_(1) x + c_(1) = 0 and, a_(2) x^(2) + b_(2) x + c_(2) = 0 have a common root, then the value of (a_(1) b_(2) - a_(2) b_(1)) (b_(1) c_(2) - b_(2) c_(1)) , is

    A
    `-(a_(1) c_(2) - a_(2) c_(1))^(2)`
    B
    `(a_(1) a_(2) - c_(1) c_(2))^(2)`
    C
    `(a_(1) c_(1) - a_(2) c_(2))^(2)`
    D
    `(a_(1) c_(2) - c_(1) a_(2))^(2)`

  • If the ratio of the roots of a_(1)x^(2) +b_(1)x+c_(1)=0 be equal to the ratio of the roots of a_(2)x^(2)+b_(2)+c_(2)=0," then "(a_(1))/(a_(2)), (b_(1))/(b_(2)), (c_(1))/(c_(2)) are in

    A
    A.P.
    B
    G.P.
    C
    H.P.
    D
    None

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