help!

The eqn x2+bx+c = 0 has distinct roots. It 2 is subtracted from each root, the results are reciprocal of the original roots. Then what is the value of (b2+c2+bc) ??

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Ricky ·

If " 2 " is subtracted from each root , then the eqn . having those two roots is -

( x - 2 ) 2 + b ( x - 2 ) + c = 0

or , x 2 + x ( b - 4 ) + c + 4 - 2 b = 0

The roots of the eqn. having the roots which are reciprocals to that of the given roots is -

b x 2 + c x + 1 = 0

By comparingthe sum of the roots and the product of the roots ,

b - 4 = - cb

c + 4 - 2 b = 1b

Now you can solve for " b " and " c " .

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