Question:medium

Given quadratic equation is \( x^{2} - |x| - 30 = 0 \). Then which of the following statements is/are incorrect?

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Substitute \( u = |x| \) to turn the equation into a simple quadratic in \( u \), then check which linear statements actually match the roots.
Updated On: Jul 21, 2026
  • \( x - 6 = 0 \)
  • \( x + 6 = 0 \)
  • \( x + 5 = 0 \)
  • Both (c) and (d)
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The Correct Option is D

Solution and Explanation

Solve the equation directly for $ x $ and test each printed statement by substitution into the original equation.

  1. x - 6 = 0: gives $ x=6 $; checking, $ 6^2-|6|-30=36-6-30=0 $, so this statement is correct.
  2. x + 6 = 0: gives $ x=-6 $; checking, $ (-6)^2-|-6|-30=36-6-30=0 $, so this statement is correct too.
  3. x + 5 = 0: gives $ x=-5 $; checking, $ (-5)^2-|-5|-30=25-5-30=-10 $, which is not 0, so this statement is incorrect.
  4. x + 7 = 0: gives $ x=-7 $; checking, $ (-7)^2-|-7|-30=49-7-30=12 $, which is also not 0, so this statement is incorrect.

The equation $ x^2-|x|-30=0 $ has only the roots $ x=6 $ and $ x=-6 $, so statements (c) and (d) both fail together, matching that combined option.

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