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If one root of the x …

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If one root of the x square-x-k=0 be the square of other than k is equal to the

    • Posted by Harshit Mehta 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    The given equation is:
    x2 - x + k = 0
     As it is given that 3 is root of the equation x2 - x + k = 0, therefore we have:
    (3)2 - 3 + k = 0
    {tex}\Rightarrow{/tex} 9 - 3 + k = 0
    {tex}\Rightarrow{/tex} 6 + k = 0
    {tex}\Rightarrow{/tex} k = - 6
    For p = - 6 the other given equation becomes:
    x2 - 6(2x - 6 + 2) + p = 0
    {tex}\Rightarrow{/tex} x2 -12x + 24 + p = 0
    This is the form of ax2 + bx + c = 0,
    where a = -1, b = -12 and c = 24 + p
    Since the given equation has equal roots, therefore D = 0.
    i.e.,  b2 - 4ac = 0
    {tex}\Rightarrow{/tex} (-12)2 - 4(1)(24 + p) = 0
    {tex}\Rightarrow{/tex} 144 - 96 - 4p = 0
    {tex}\Rightarrow{/tex} 48 - 4p = 0
    {tex}\Rightarrow{/tex} 4p = 48
    {tex}\Rightarrow{/tex} p = 12
    Hence, the value of p is 12.

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