State true or false. The discriminant for general quadratic equation $a x^{2} + b x + c = 0$ is $b^{2} - 4 a c$ .

True

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False

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Solution

The correct option is A
True

$a x^{2} + b x + c = 0$

Roots of equation = $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

= $\frac{- b}{2 a}$ + $\frac{\sqrt{b^{2} - 4 a c}}{2 a}$ , $\frac{- b}{2 a}$ - $\frac{\sqrt{b^{2} - 4 a c}}{2 a}$

$\Rightarrow (b^{2} - 4 a c)$ term discriminates between the 2 roots of the equation.

$\Rightarrow$ Discriminant = $b^{2} - 4 a c$

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