for the given polynomial: b(x)=6x^4-23x^3+x^2+5x-1

Question

1. find the maximum possible numbers of the positive and the negative roots
2. find all the integer roots
3. find the non- integer real roots
4. find the complex roots

Answer 1

desmos.com/calculator/uwnezpncme

Answer 2

Use Descartes' Sign Rule

More info: https://mathworld.wolfram.com/DescartesSignRule.html#:~:text=A%20method%20of%20determining%20the,real%20roots%20of%20a%20polynomial.&text=Since%20there%20are%20three%20sign,of%20three%20possible%20positive%20roots.&text=In%20this%20example%2C%20there%20are,maximum%20of%20four%20negative%20roots.