The number of solutions to the equation $∣ ∣ 2 x^{2} - 5 x + 3 ∣ ∣ + (x - 1) = 0$ is :

1

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2

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0

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infinite

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Solution

The correct option is B $2$
$∣ ∣ {2 x}^{2} - 5 x + 3 ∣ ∣ + (x - 1) = 0$
let ${2 x}^{2} - 5 x + 3 > 0$ ${2 x}^{2} - 5 x + 3 < 0$
${2 x}^{2} - 5 x + 3 + x - 1 = 0$ $- {2 x}^{2} + 5 x - 3 + x - 1 = 0$
${2 x}^{2} - 4 x + 2 = 0$ $- {2 x}^{2} + 6 x - 4 = 0$
$x^{2} - 2 x + 1 = 0$ $x^{2} - 3 x + 2 = 0$
${(x - 1)}^{2} = 0$ $x^{2} - 2 x - x + 2 = 0$
$x = 1$ $x (x - 2) - 1 (x - 2) = 0$
$x = 1, 2$
$∴$ , No. of solutions are $2$ i.e $1$ & $2$ .

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