Which of the following quadratics is irreducible?

2 x^{2} - 5 x + 3

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2 x^{2} - 5 x - 3

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5 x^{2} - 2 x + 3

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5 x^{2} - 2 x - 3

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Solution

The correct option is C $5 x^{2} - 2 x + 3$
We can check by comparing the D of quadratic equations with their relation with 0

$2 x^{2} - 5 x + 3 = 0$
$D = (- 5)^{2} - 4 (2) (3) = 25 - 24 = 1 > 0$
Reducible

$2 x^{2} - 5 x - 3 = 0$
$D = (- 5)^{2} - 4 (2) (- 3) = 25 + 24 = 49 > 0$
Reducible

$5 x^{2} - 2 x + 3 = 0$
$D = (- 2)^{2} - 4 (5) (3) = 4 - 60 = - 56 < 0$
Irreducible

$5 x^{2} - 2 x - 3 = 0$
$D = (- 2)^{2} - 4 (5) (- 3) = 4 + 60 = 64 > 0$
Rreducible

Therefore correct option is C

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