Question

Determine nature of the roots of x2-2x-3=0 ?​

Answer 1

Solution:-

Given equation

$\rm \to {x}^{2} - 2x - 3 = 0$

Now compare with

$\rm \: \to \: a {x}^{2} + bx + c = 0$

So

$\rm \: a = 1,b = - 2 \: \: and \: \: c = - 3$

To find the nature of roots first find D

$\boxed{ \rm \: D = {b}^{2} - 4ac}$

$\rm \: D = { - 2}^{2} - 4 \times 1 \times - 3$

$\rm \: D = 4 + 12$

$\rm \: D = 16$

when D > 0 the nature of root is real

Now find the value of x

using quadratic formula

$\boxed{ \rm \: x = \dfrac{ - b \pm \sqrt{D} }{2a} }$

So

$\rm \: a = 1,b = - 2 \: \: ,\: \: c = - 3 \: and \: D = 16$

$\rm \: x = \dfrac{ - ( - 2) \pm \sqrt{16} }{2 \times 1}$

$\rm \: x = \dfrac{2 + 4}{2} \: and \: \: x = \dfrac{2 - 4}{2}$

$\rm \: x = \dfrac{6}{2} \: \: \: and \: x = \dfrac{ - 2}{2}$

$\rm \: x = 3 \: and \: \: x = - 1$