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2015-04-22T15:33:51+05:30

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P(x) = 2 x⁴ + x³ - 14 x² - 19 x - 6
   The number of sign changes in the coefficients : of P(x) = 1
   the number of sign changes in the coefficients of  P(-x) = 3

There are atmost 3 negative real roots and 1 positive real root.

  two roots or zeros are :  -2 and -1.
  So (x+2) and (x+1) are the factors of  P(x).

     P(x) = (x² + 3 x + 2) (a x² + b x + c) = 2 x⁴ + x³ - 14 x² - 19 x - 6

   comparing both sides we can say that:
           a = 2     and  c = - 3.
   the coefficient of  x³ on both sides are :    3 a + b = 1
               b = -5

  The roots of :  2 x² - 5 x - 3  = 0
                   (2 x + 1 ) ( x - 3 ) = 0
                     x = - 1/2    or  3

2 5 2