Without solving examine the nature of the roots of the equation:
$6 x^{2} - 5 x - 6 = 0$

Open in App

Solution

Step 1: Nature of the roots of an equation.
The given equation is as follows:
$6 x^{2} - 5 x - 6 = 0$
Compare the co-efficient of the given equation with $a x^{2} + b x + c = 0$ to get:
$a = 6, b = - 5 and c = - 6$
Now solving for discriminant as:
$\begin{array}{rcl} ∴ D & = & {(b)}^{2} - 4 a c \\ = & {(- 5)}^{2} - 4 (6) (- 6) \\ D & = & 169 > 0 \end{array}$
Hence, the roots of the given equation are real and distinct.

Suggest Corrections

Similar questions

Without solving, examine the nature of roots of the equations 2 $x^{2}$ – 5x + 5 = 0

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

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

Without solving, examine the nature of roots of the equation.

4 $x^{2}$ – 4x + 1 = 0 [2 MARKS]

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

$3 x^{2} + 2 x - 1 = 0$

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

$x^{2} + p x - q^{2} = 0$

Join BYJU'S Learning Program