Determine the roots of the following polynomials:

(a) $\quad p_{1}(x)=x^{7}+8 x^{6}+5 x^{5}+4 x^{4}+3 x^{3}+2 x^{2}+x+1$(b) $p_{2}(x)=x^{6}-7 x^{6}+7 x^{5}+15 x^{4}-10 x^{3}-8 x^{2}+7 x+15$

(c) $p_{3}(x)=x^{5}-13 x^{4}+10 x^{3}+12 x^{2}+8 x-15$

(d) $p_{4}(x)=x^{4}+7 x^{3}+12 x^{2}-25 x+8$

(e) $\quad p_{5}(x)=x^{3}+15 x^{2}-23 x+105$

(f) $p_{6}(x)=x^{2}-18 x+23$

(g) $\quad p_{7}(x)=x+7$