Find the value of k for which the roots of the quadratic equation kx(x – 2) + 6 = 0 are equal. *If –4 is a root of the equation x² + px – 4

Question

Find the value of k for which the roots of the quadratic equation kx(x – 2) + 6 = 0 are equal. *If –4 is a root of the equation x² + px – 4 = 0 and the equation x² + px + q = 0 has equal roots, find the values of p and q. *

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Amara 1 month 2021-08-12T15:13:47+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-12T15:14:55+00:00

    Answer:

    x

    2

    +px+1=0

    a+b=−p

    ab=1

    x

    2

    +qx+1=0

    c+d=−q

    cd=1

    (a−c)(b−c)=ab−(a+b)c+c

    2

    (1+pc+c

    2

    )

    (a+d)(b+d)=ab+(a+b)d+d

    2

    =(1−pd+d

    2

    )

    ∴(1+pc+c

    2

    )(1−pd+d

    2

    )

    =1−pd+d

    2

    +pc−p

    2

    cd+c

    2

    −pc

    2

    d+c

    2

    d

    2

    =1+c

    2

    +d

    2

    +pc−pc

    2

    d+pcd

    2

    −pd+p

    2

    cd+c

    2

    d

    2

    =1+c

    2

    +d

    2

    +pc−pc+pd−pd+p

    2

    +1

    =2+p

    2

    +(c+d)

    2

    −2d

    =2+p

    2

    +q

    2

    −2

    =p

    2

    +q

    2

    q

    2

    −p

    2

    (a−c)(b−c)(a+d)(b+d)

    =

    q

    2

    −p

    2

    q

    2

    +p

    2

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