Exactly 3 solutions are demanded

Algebra Level 5

If the equation $|x^2-5x+6|-\lambda.x+7\lambda=0$ has exactly $3$ real solutions, then $\lambda$ is equal to ?

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-9-4\sqrt{5}

All the given values.

-9+4\sqrt{5}

-7+\sqrt{23}

-7-\sqrt{23}