Consider the polynomial f(x) = 5x4+ 3x2+ x + 19. how many complex solutions does the polynomial have? consider the polynomial f(x)=5x5-8x4+19x2-3. this polynomial has zero's with multiplicity 1 and complex zero's ?

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.

there are 4 complex solutions

3 real zeros and 2 complex zeros

Step-by-step explanation:

the answer is 8/21

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