What does descartes' rule of signs tell you about the possible number of positive real zeros and the possible number of negative real zeros of the function?
f(x)=3x^5-3x^2+x-4

the possible number of positive real zeros is
what? the possible number of negative real zeros is
what?

Step-by-step explanation:

The signs of the coefficients of the given terms are ...

  +  -  +  -

There are three sign changes, so the number of positive real zeros is 3 or 1.

When odd-degree terms have their signs changed, the signs become ...

  -  -  -  -

There are no sign changes, hence no negative real zeros.

_____

A graph confirms this evaluation.

the thermometer is precise but not accurate

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)