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Question Number 215820 by Jubr last updated on 18/Jan/25

Commented by A5T last updated on 18/Jan/25

$$\mathrm{This}\mathrm{is}\mathrm{not}\mathrm{generally}\mathrm{true},\mathrm{it}\mathrm{fails}\mathrm{when}\mathrm{c}=0.$$

Answered by Rasheed.Sindhi last updated on 18/Jan/25

$${ax}^2+bx+c=0$$$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\times \frac{-b\mp \sqrt{b^2-4ac}}{-b\mp \sqrt{b^2-4ac}}$$$$x=\frac{b^2-(b^2-4ac)}{2a(-b\mp \sqrt{b^2-4ac})}$$$$=\frac{4ac}{2a(-b\mp \sqrt{b^2-4ac})}$$$$=\frac{2c}{-b\mp \sqrt{b^2-4ac}}$$

Commented by Jubr last updated on 19/Jan/25

$$Thankssir.$$

Answered by A5T last updated on 18/Jan/25

$${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$$$$\mathrm{x}\ne 0\Rightarrow \mathrm{c}{\left(\frac{1}{\mathrm{x}}\right)}^2+\mathrm{b}\left(\frac{1}{\mathrm{x}}\right)+\mathrm{a}=0$$$$\Rightarrow \frac{1}{\mathrm{x}}=\frac{-\mathrm{b}\underset{-}{+}\sqrt{{\mathrm{b}}^2-4\mathrm{ca}}}{2\mathrm{c}}(\mathrm{c}\ne 0)$$$$\Rightarrow \mathrm{x}=\frac{2\mathrm{c}}{-\mathrm{b}\underset{-}{+}\sqrt{{\mathrm{b}}^2-4\mathrm{ac}}}\mathrm{when}\mathrm{c}\ne 0\mathrm{and}\mathrm{x}\ne 0$$

Commented by Jubr last updated on 19/Jan/25

$$Thankssir$$

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