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Question Number 34425 by Vijay kumar prasad last updated on 06/May/18

$$a,b,c\in R,a\ne 0\mathrm{and}\mathrm{the}\mathrm{quadratic}$$$$\mathrm{equation}{ax}^2+bx+c=0\mathrm{has}\mathrm{no}\mathrm{real}$$$$\mathrm{roots},\mathrm{then}$$

Answered by MJS last updated on 06/May/18

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$$$b^2-4ac<0\Rightarrow \mathrm{no}\mathrm{real}\mathrm{roots}$$$$b^2-4ac=0\Rightarrow \mathrm{exactly}\mathrm{one}\mathrm{real}\mathrm{root}$$$$b^2-4ac>0\Rightarrow \mathrm{two}\mathrm{real}\mathrm{roots}$$

Answered by Rio Mike last updated on 06/May/18

$$b^2-4ac=0$$

Commented by MJS last updated on 06/May/18

$$\mathrm{in}\mathrm{this}\mathrm{case}\mathrm{you}\mathrm{have}1\mathrm{real}\mathrm{root}$$

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