As is known, a quadratic equation has no more than two roots. Can the equation $\$[x \wedge 2]+p x+q=0 \$$ for \$p \ne 0 have more than 100 roots? (\$ \$x^2]\$ denotes the greatest integer not exceeding \$x^2\$.)
Consider, for example, the equation $\$\left[x^{\wedge} 2\right]-100 x+2500=0 \$$. It has 199 roots of the form $\$ 50+\backslash f r a c\{k\}\{100\} \$$ (where \$k = - 99\$, \$- 98, ···, 99\$). Indeed, \$\$lleft[left(50 +|frac\{k\}

$\{100\} \backslash$ right)^2\right]=\left[2500+k+\left(|frac $\{k\}\{100\} \backslash$ right)^2\right]=2500+k=100|cdot\left(50 +|frac $\{k\}$

$\{100\}$ (right)-2500.\$ $\$ 2$

## Answer

It can.
