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STD 11 - 4.2 Quadratic equations and inequations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.2 Quadratic equations and inequations4 Marks
MCQ
For the equation $|{x^2}| + |x| - 6 = 0$, the roots are
  • A
    One and only one real number
  • B
    Real with sum one
  • ✓
    Real with sum zero
  • D
    Real with product zero
✓

Answer

Correct option: C.
Real with sum zero
c
(c) When $x < 0$, $|x| = - x$

Equation is ${x^2} - x - 6 = 0 \Rightarrow x = - 2,\,3$

$\;x < 0,\;\therefore \;x =  - 2$is the solution.

When $x \ge 0$,$|x| = x$

$\therefore $ Equation is${x^2} + x - 6 = 0 \Rightarrow x = 2, - 3$

$x \ge 0$,  $x = 2$ is the solution.

Hence $x = 2$, $ - 2$ are the solutions and their sum is zero.

Aliter : $|{x^2}| + |x| - 6 = 0$

==> $(|x| + 3)(|x| - 2) = 0$

==> $|x| = - 3$, which is not possible and $|x| = 2$

==> $x = \pm 2$.

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