Question

For √(3x^2 )+5x-2√3=0, discuss its nature of roots.

Answer 1

To justify the nature of the roots of the above equation

Given,

$\sf{ \sqrt{3}x {}^{2} + 5x - 2 \sqrt{3} = 0 }$

The nature of the roots of a equation are determined by its discriminant,D

•If the discriminant is:

1. Greater than zero,D>0,has real and distinct roots

2. Equal to zero,D=0,has real and equal roots

3. Less than zero,D<0,has non real roots or imaginary roots

Comparing with ax²+bx+c=0,

a=√3,b=5 and c= -2√3

Discriminant,D=b²-4ac

=(5)²-4(√3)(-2√3)

=25+24

=49

As D<0,the given equation has real and distinct roots