[tex]a)~~P(X) = X^2+10X+25 = X^2+2\cdot X \cdot 5 + 5^2 = (x+5)^2 \\
X_1 = -5 \\
X_2 = -5 \\
\Longrightarrow~~\text{Ordinul de multiplicitate al radacinii } \alpha = -5 ~este~ \boxed{2} \\ \\
b)~~P(X)= X^3 + 15X^2+75X +125= \\
= X^3 + 3 \cdot 5 \cdot X^2+3 \cdot 5^2 \cdot X +5^3= (X+5)^3 \\
X_1 = -5 \\
X_2 = -5 \\
X_3 = -5 \\
\Longrightarrow~~\text{Ordinul de multiplicitate al radacinii } \alpha = -5 ~este~ \boxed{3} [/tex]
[tex]c)~~P(X)= X^4 - 625= \\ (X^2 - 25)(X^2 + 25) = (X+5)(X-5)(X^2+25) \\
X_1 = -5 \\
X_2 = 5 \\
X_3 , ~X_4 = radacini ~complex-conjugate \\
\Longrightarrow~~\text{Ordinul de multiplicitate al radacinii } \alpha = -5 ~este~ \boxed{1} [/tex]
