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Daniel [21]
3 years ago
9

Consider the polynomial f(x) = 5x4+ 3x2+ x + 19. How many complex solutions does the polynomial have?

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
5 0

Answer:

  1. there are 4 complex solutions
  2. 3 real zeros and 2 complex zeros

Step-by-step explanation:

1. Descarte's rule of signs tells you there are 0 positive real roots and 0 or 2 negative real roots. (for positive x, signs are ++++ so have no changes; for negative x, signs are ++-+, so have 2 changes.) A graph shows no real roots.

2. There are 3 sign changes in the given polynomial, so 3 or 1 positive real roots. When the sign of x is changed, there are 2 sign changes, so 0 or 2 negative real roots. A graph shows 2 negative and one positive real root (for a total of 3), so the remaining 2 roots are complex.

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