How to find the number of real roots of any equation?

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Solution

Number of real roots will depend on the value of 'D'.
Sag, the egn is $a x^{2} + b x + c = 0$
$D = b^{2} - 4 a c$
and roots are $\frac{- b \pm \sqrt{b^{2}} - 4 a c}{2 a}$
(1) If D > 0 $\Rightarrow$ Real & distinet roots
(2) If D = 0 $\Rightarrow$ Real & equal roots
(3) If D < 0 $\Rightarrow$ Imaginary roots.

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