f(x) 3x^3 + 10x^2 + 10x +7. find the interval of uni length which contains the root

Question

anonymous · Answer

this one actually factors, but you can try $f(-1)$ and $f(-2)$ and see that one is positive, the other negative

anonymous · Answer

this is called the intermediate value theorem the results of the two y values given by satellite are between 0 $$f(-1)<f(0)<-2)$$
then there is a number c in the interval (-1,-2) such that $$f(c)=0$$

anonymous · Answer

$$
3 x^3+10 x^2+10 x+7=(3 x+7)
   \left(x^2+x+1\right)\

x= -\frac 7 3 
$$

anonymous · Answer

$$
[-\frac 7 3 - \frac 1 2,-\frac 7 3 + \frac 1 2]=[-\frac {17}6,-\frac {11}6]
$$