Question

Find the discriminant of the quadratic equation $2x^2-6x+3=0$, and hence find the nature of its roots.

Answer 1

Given quadratic equation is $2x^2-6x+3=0$

The standard quadratic equation is $a{x}^2+bx+c=0$

Here $a=2,b=-6,c=3$

As we know that,

Discriminant $\left(D\right)=b^2-4ac$

$\therefore D={(-6)}^2-4\times 2\times 3$

$\Rightarrow D=36-24=12>0$

When discriminant is positive and greater than 0, then roots will be real and distinct (Different).

Hence, for the given quadratic equation the roots are real and different.