Without solving, examine the nature of the roots of the equation:
$3 x^{2} + 2 x - 1 = 0$

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Solution

Step 1: Nature of the roots of an equation.
The given equation is as follows:
$3 x^{2} + 2 x - 1 = 0$
Compare the co-efficient of the given equation with $a x^{2} + b x + c = 0$ to get:
$a = 3, b = 2 and c = - 1$
Now solving for discriminant as:
$\begin{array}{rcl} ∴ D & = & {(b)}^{2} - 4 a c \\ = & {(2)}^{2} - 4 (3) (- 1) \\ D & = & 16 > 0 \end{array}$
Hence, the roots of the given equation are real and distinct.

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