The roots of |x - 2|^2 + |x - 2| - 6 = 0 are | vedclass

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(A) Let $y = |x - 2|$. Since $|x - 2| \ge 0$,we have $y \ge 0$.The equation becomes $y^2 + y - 6 = 0$.Factoring the quadratic equation: $(y + 3)(y - 2

Vedclass · Accepted Answer

$0, 4$

Vedclass · Answer

(A) Let $y = |x - 2|$. Since $|x - 2| \ge 0$,we have $y \ge 0$.The equation becomes $y^2 + y - 6 = 0$.Factoring the quadratic equation: $(y + 3)(y - 2) = 0$.This gives $y = -3$ or $y = 2$.Since $y \ge 0$,we discard $y = -3$. Thus,$y = 2$.Substituting back,$|x - 2| = 2$.This implies $x - 2 = 2$ or $x - 2 = -2$.Solving these,$x = 4$ or $x = 0$.Therefore,the roots are $0$ and $4$.

The roots of $|x - 2|^2 + |x - 2| - 6 = 0$ are

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