1.1. For what least natural value of \( b \) does the equation

$$
x^{2}+b x+25=0
$$

have at least one root?
Answer: 10

Solution. The equation has at least one root if and only if the discriminant $D=b^{2}-4 \cdot 25=$ $=b^{2}-100$ is greater than or equal to 0. For positive $b$, this condition is equivalent to the condition $b \geqslant 10$.