(B) Given equation: $|x-2|^2+|x-2|-2=0$ Let $y = |x-2|$. Since $|x-2| \geq 0$,we must have $y \geq 0$. The equation becomes $y^2 + y - 2 = 0$. Factori

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(B) Given equation: $|x-2|^2+|x-2|-2=0$ Let $y = |x-2|$. Since $|x-2| \geq 0$,we must have $y \geq 0$. The equation becomes $y^2 + y - 2 = 0$. Factoring the quadratic: $(y+2)(y-1) = 0$. This gives $y = -2$ or $y = 1$. Since $y \geq 0$,we discard $y = -2$. Thus,$|x-2| = 1$. This implies $x-2 = 1$ or $x-2 = -1$. Solving for $x$: $x = 3$ or $x = 1$. The sum of the real roots is $3 + 1 = 4$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

Medium

The sum of all the real roots of the equation $|x-2|^2+|x-2|-2=0$ is

AP EAMCET 2022 All AP EAMCET

A
$7$
B
$4$
C
$1$
D
None of these

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