Question

найдите произведение корней уравнения x3+7x+12x+10/x2+8x+15=2

Answer 1

$\frac{x^3+7x^2+12x+10}{x^2+8x+15}=2\Leftrightarrow \frac{\left ( x^2+2x+2 \right )\left ( x+5 \right )}{\left ( x+3 \right )\left ( x+5 \right )}=2\\x^2+2x+2-2x-6=0\Leftrightarrow x^2-4=0\Rightarrow x=\pm 2\\x_1\cdot x_2=-4$