SOLUTION: Can you help me with this? Thanks What is the difference of the product and the sum of real solutions from {{{ x^4 + 5x^3 + 5x^2 - 3x -8 }}} a. -11 b. -1 c. 0 d. 1 e. 11

Algebra ->  Equations -> SOLUTION: Can you help me with this? Thanks What is the difference of the product and the sum of real solutions from {{{ x^4 + 5x^3 + 5x^2 - 3x -8 }}} a. -11 b. -1 c. 0 d. 1 e. 11      Log On


   



Question 1006384: Can you help me with this? Thanks
What is the difference of the product and the sum of real solutions from +x%5E4+%2B+5x%5E3+%2B+5x%5E2+-+3x+-8+
a. -11
b. -1
c. 0
d. 1
e. 11

Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hello,

where are numerous mistakes in formulation of the problem.

1. You wrote a polynomial, not an equation.
   Therefore, about what solutions are you talking?
   In this case, you should talk about the roots of the polynomial, not about the solutions.

2. You are asking about real solutions, which is wrong again.
   Question should go about all the roots, real and complex.
   Then the question makes sense. Otherwise, it doesn't make sense.

3. The sum of all roots is the coefficient at x%5E3 with the opposite sign, i.e. -5.
   The product of the roots is equal to the constant term, i.e. -8.
   Hence, "the difference of the product and the sum of" the roots of the given polynomial is (-8) - (-5) = -8 + 5 = -3.

4. Amazingly, all positions in your request, including the options for the answer, are wrong.