The roots of the equation

Question:

The roots of the equation $2 x^{2}-6 x+3=0$ are

(a) real, unequal and rational
(b) real, unequal and irrational
(c) real and equal
(d) imaginary

Solution:

(b) real, unequal and irrational

$\because D=\left(b^{2}-4 a c\right)$

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

$=36-24$

$=12$

12 is greater than 0 and it is not a perfect square; therefore, the roots of the equation are real, unequal and irrational.