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

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Solution

(b) real, unequal and irrational

$∵ D = (b^{2} - 4 a c) = {(- 6)}^{2} - 4 \times 2 \times 3 = 36 - 24 = 12 12 is greater than 0 and it is not a perfect square; therefore, the roots of the equation are real, unequal and irrational .$

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