InterviewSolution
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InterviewSolution
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If the cubic `2x^3=9x^2+12 x+k=0`has two equal roots then minimum value of `|k|`is______. |
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Answer» Correct Answer - 5 We have `2x^(3)-9x^(2)+12x +k =0` Let the roots are `alpha,alpha, beta` `2alpha+beta=(9)/(2)" "(1)` `alpha + 2alphabet=(12)/(2)=6" "(2)` are `alpha^(2)beta=-(k)/(2)" "(3)` putting `beta = ((9)/(2)-2alpha)` from (1) in (2), we have `alpha^(2)+2alpha((9)/(2)-2alpha)=6` or `alpha^(2)+9alpha-4alpha^(2)=6` or `3alpha^(2)-9alpha+6=0` or `alpha^(2)-3alpha+2=0` or `(alpha-2)(alpha-1)=0rArralpha=2 or1` `if alpha=2, "then "alpha=(1)/(2),` `if alpha=1, " then " beta=(5)/(2)` `therefore k=-2(2^(2))(1)/(2)=-4` `or k=-2 (1^(2))((5)/(2))=-5` |
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