Q.

If  x3+3x2-9x+c is of the form x-α2x-β then the positive value of c is ____

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answer is 5.

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Detailed Solution

Here   x=α  isarepeatedrootoftheequation  fx=0.Hence,  x=α  isalsoarootoftheequation  f'x=0,  i.e.,            3x2+6x-9=0or  x2+2x-3=0   or  x+3x-1=0has  the   root  α  once  which  can  be  eitheer  -3  or 1.If  α=1,   then  fx=0   gives  c-5=0  or  c=5.If  α=-3,  then  fx=0   gives   -27+27+27+c=0∴   c=-27
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