Consider the polynomial f(x) = 5x4+ 3x2+ x + 19. How many complex solutions does the polynomial have?
1 answer:
Answer:
- there are 4 complex solutions
- 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.
You might be interested in
An equal sign is a symbol in mathematics.
It is to indicate that the given terms are <span>equal.
It is also used to </span>indicate a mathematical <span>equality.
An equal sign looks like ( </span>
) this.
It is to indicate that the given terms are <span>equal.
It is also used to </span>indicate a mathematical <span>equality.
An equal sign looks like ( </span>