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4.2 Quadratic equations and inequations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.2 Quadratic equations and inequations1 Mark
MCQ
If $|x - 2| + |x - 3| = 7$, then $x =$
  • A
    $6$
  • B
    $-1$
  • ✓
    $6$  or $-1$
  • D
    None of these
✓

Answer

Correct option: C.
$6$  or $-1$
c
(c) Here $x = 2$ and $3$ are the critical points.

When $x < 2,|x - 2| = - (x - 2),|x - 3| = - (x - 3)$

$\therefore $ The given equation reduces to $2 - x + 3 - x = 7$

==> $x = - 1 < 2$

$\therefore $ $x = - 1$ is a solution.

When $2 \le x < 3,\,\,|x - 2| = x - 2,|x - 3| = - (x - 3)$

$\therefore $ The equation reduces to $x - 2 + 3 - x = 7$==> $1=7$

$\therefore $ No solution in this case.

When $x \ge 3$, the equation reduces to

$x - 2 + x - 3 = 7$ ==> $x = 6 > 3$

Hence we get, $x = 6$or $-1$

Trick : By inspection, we have that both the values $x = 6, - 1$ satisfy the given equation.

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