x^3-7x^2+14x-6 identify all real roots rational root theorum?

Question

also 5/3x^3+8/3x^2-4/3x

x^5-4x^4-2x^3+4x^2+x

all in rational root theorum

Answer 1

x³ − 7·x² + 14·x − 6
There is either three positive real roots... or there is one positive real root and two non-real roots. The only possible real rational roots are positive 1, 2, 3, and 6

x^5 − 4·x^4 − 2·x³ + 4·x² + x
There is either two positive real roots, one negative real root, and two non-real roots... or there is one negative real root and four non-real roots. The only possible real rational roots are positive and/or negative 1

Answer 2

X=3 is a root so
=(x-3) ( x^2-4x+2) == roots 3 and 2+-sqrt2
2)x=0 is a rootso
x^4-4x^3-2x^2+4x +1=0
only possible rational roots 1 and -1
Testing 1 is a tootso factoting
(x-1)(x^3-3x^2-5x-1)=0The second factor has root x=-1
(x-1)(x+1)(x^2-4x-1)
x= ((4+-sqrt(20))/2 = 2+-sqrt5