Solve:
$| x^{2} - 3 x + 2 | = 2$

0, 3, \frac{2 \pm \sqrt{25} i}{2}

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0, 3, \frac{- 2 \pm \sqrt{25} i}{2}

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0, 3, \frac{3 \pm \sqrt{7} i}{2}

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0, 3, \frac{- 3 \pm \sqrt{7} i}{2}

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Solution

The correct option is C $0, 3, \frac{3 \pm \sqrt{7} i}{2}$
$∣ ∣ x^{2} - 3 x + 2 ∣ ∣ = 2$
$\Rightarrow x^{2} - 3 x + 2 = \pm 2$

Case (1):

$x^{2} - 3 x + 2 = 2$
$x^{2} - 3 x = 0$
$x (x - 3) = 0$

$x = 0, 3$

Case (2):

$x^{2} - 3 x + 2 = - 2$
$x^{2} - 3 x + 4 = 0$

The roots of the quadratic equation $A x^{2} + B x + C = 0$ are

$x = \frac{- B \pm \sqrt{B^{2} - 4 A C}}{2 A}$

for the given equation, $B^{2} - 4 A C = (- 3)^{2} - 4 (1) (4) = - 7$

So,
$x = \frac{3 \pm \sqrt{- 7}}{2}$

$x = \frac{3 \pm \sqrt{7} i}{2}$

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