解決4alpha^2x^2+4alphabetax=-4alphagamma |Microsoft數學求解器

$$4 \alpha ^ { 2 } x ^ { 2 } + 4 \alpha \beta x = - 4 \alpha \gamma$$

解 x (復數求解)

$$\left\{\begin{matrix}x\in \mathrm{C}\text{, }&\alpha =0\\x=-\frac{-\sqrt{\beta ^{2}-4\alpha \gamma }+\beta }{2\alpha }\text{; }x=-\frac{\sqrt{\beta ^{2}-4\alpha \gamma }+\beta }{2\alpha }\text{, }&\alpha \neq 0\end{matrix}\right.$$

解 α (復數求解)

$$\left\{\begin{matrix}\\\alpha =0\text{, }&\text{unconditionally}\\\alpha =-\frac{x\beta +\gamma }{x^{2}}\text{, }&x\neq 0\\\alpha \in \mathrm{C}\text{, }&\gamma =0\text{ and }x=0\end{matrix}\right.$$

解 α

$$\left\{\begin{matrix}\\\alpha =0\text{, }&\text{unconditionally}\\\alpha =-\frac{x\beta +\gamma }{x^{2}}\text{, }&x\neq 0\\\alpha \in \mathrm{R}\text{, }&\gamma =0\text{ and }x=0\end{matrix}\right.$$