anonymous 4 years ago find all zeros of the poynolminal function or solve the given polynomial equation, use the rational zero theorem descartes rule of sign and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root $x^3-4x^2-7x+10$

1. anonymous

$x^3-4x^2-7x+10=0$

2. anonymous

changing sign is 2 so it has 2 positive root or zero positive root

3. anonymous

$f(-x)=-x^3-4x^2+7x+10$ so it has 1 negative root

4. anonymous

factor of 10 is $\pm1,2,5,10$

5. anonymous

factor of 1 is$\pm1$

6. anonymous

roots might be $\pm1,2,5,10$

7. anonymous

f(1)=0 so 1 is root of f(x)

8. anonymous

$\frac{x^3-4x^2-7x+10}{x-1}$

9. anonymous

$\frac{x^3-4x^2-7x+10}{x-1}=x^2-3x-10$

10. anonymous

$x^3-4x^2-7x+10=(x-1)(x^2-3x-10)$ =(x-1)(x-5)(x+2)=0

11. anonymous

$x _1=1, x_2=5, x_3=-2$

12. anonymous