Question

Use Descartes’ Rule of Signs to describe all possibilities for the number of positive, negative and imaginary
zeros of

P (x) = x4 + x3 + x2 + x + 12

Answer 1

there is no change of sign of the coefficients, (they are all positive) so there is no positive zero
now compute \(p(-x)=x^4-x^3+x^2-x+12\) and you see 4 changes in sign, telling you there are either 4, 2 or no negative zeros

Answer 2

there are 4 zeros altogether, including complex zeros, so possibilities are
4 negative
2 negative, 2 complex
0 negative 4 complex

Answer 3

in fact there are 4 complex, but descartes rule of sign does not tell you that

Answer 4

cool,so is complex the same as imaginary ?in the notes i have there are three columns, positive,negative and imaginary zeros