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a,b,c in R alpha is a root of a^...

a,b,c ` in R alpha ` is a root of ` a^2 x^2 +bx +c=0 beta ` is a root of ` a^2 x^2 - bx - c=0` and ` gamma` is a root of ` a^2 x^2 + 2 bx + 2 c=0` then

A

A,B,C,D

B

B,D,C,A

C

A,C,B,D

D

D,B,A,C

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Let a,b,c be real numbers a ne 0 if alpha is a roots of a^2 x^2 + bx +c=0 , beta is a roots of a^2 x^2 -bx -c=0 and 0 lt alpha lt beta , then the equation a^2 x^2 + 2bx + 2c =0 has a root gamma has a root gamma that always satisfies

    A
    `gamma = ( alpha + beta ) //2`
    B
    `gamma = (alpha + beta /2)`
    C
    `gamma = alpha `
    D
    `alpha lt gamma lt beta `

  • The condition that a root of ax^2+bx +c=0 may be the reciprocal of a root of a_1 x^2+b_1x +c_1=0 is

    A
    `(a a_1 -c c _1)^2 (ab_1+bc _1 )(a_1b +b_1c)`
    B
    `(a a _1 -c c _1 )^2 =(ab_1-bc_1)(a_1b -b _1c)`
    C
    `(a a _1 - b b _1)^2 =(ac _1 -bc _1)`
    D
    none

  • Sum of the roots of ax^(2) + bx + c = 0 is..

    A
    `c/a`
    B
    `b/a`
    C
    `a/b`
    D
    none

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