4alpha^2x^2+4alphabetax=-4alphagamma ಪರಿಹರಿಸಿ

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

x ಪರಿಹರಿಸಿ (ಸಂಕೀರ್ಣ ಪರಿಹಾರ)

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

α ಪರಿಹರಿಸಿ (ಸಂಕೀರ್ಣ ಪರಿಹಾರ)

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

x ಪರಿಹರಿಸಿ

$$\left\{\begin{matrix}x\in \mathrm{R}\text{, }&\gamma \neq 0\text{ and }\alpha =0\\x=-\sqrt{\frac{\gamma }{\alpha }}\text{, }&\alpha =\frac{\beta ^{2}}{4\gamma }\text{ and }\beta \neq 0\text{ and }\left(\beta <0\text{ or }\gamma >0\right)\text{ and }\left(\gamma <0\text{ or }\beta >0\right)\text{ and }\gamma \neq 0\\x=\sqrt{\frac{\gamma }{\alpha }}\text{, }&\alpha =\frac{\beta ^{2}}{4\gamma }\text{ and }\beta \neq 0\text{ and }\left(\beta >0\text{ or }\gamma >0\right)\text{ and }\left(\gamma <0\text{ or }\beta <0\right)\text{ and }\gamma \neq 0\\x=-\frac{\sqrt{\beta ^{2}-4\alpha \gamma }+\beta }{2\alpha }\text{; }x=-\frac{-\sqrt{\beta ^{2}-4\alpha \gamma }+\beta }{2\alpha }\text{, }&\left(\alpha \neq 0\text{ and }\alpha \leq \frac{\beta ^{2}}{4\gamma }\text{ and }\gamma >0\right)\text{ or }\left(\alpha \neq 0\text{ and }\alpha \geq \frac{\beta ^{2}}{4\gamma }\text{ and }\gamma <0\right)\text{ or }\left(\beta \neq 0\text{ and }\alpha =\frac{\beta ^{2}}{4\gamma }\text{ and }\gamma \neq 0\right)\\x\neq 0\text{, }&\gamma =0\text{ and }\alpha =0\\x=-\frac{\beta }{\alpha }\text{, }&\alpha \neq 0\text{ and }\gamma =0\text{ and }\beta \neq 0\\x=0\text{, }&\gamma =0\end{matrix}\right.$$

α ಪರಿಹರಿಸಿ

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