Question

Without solving examine the nature of the roots of the equation:

$4x^2+3x-1=0$

Answer 1

Step 1: Nature of the roots of an equation.

The given equation is as follows:

$4x^2+3x-1=0$

Compare the co-efficient of the given equation with $a{x}^2+bx+c=0$ to get:

$a=4,b=3\text{and}c=-1$

Now solving for discriminant as:

$\begin{array}{rcl}\therefore D& =& {\left(b\right)}^2-4ac\\ & =& {\left(3\right)}^2-4\left(4\right)\left(-1\right)\\ D& =& 25>0\end{array}$

Hence, the roots of the given equation are real and distinct.