Question

Given quadratic equation is x² - |x|-30 = 0. Then which of the following statements is/are incorrect?

• A. x-6=0
• B. x+6=0
• C. x+5=0
• D. x+7=0
• E. Both (c) and (d)

Answer 1

Answer: (E)

The correct answer is option (E): Both (c) and (d)

Let's analyze the given quadratic equation and the provided options. The equation is x² - |x| - 30 = 0. Because of the absolute value we consider two cases.

Case 1: x ≥ 0.
Then |x| = x and the equation becomes x² - x - 30 = 0. Factor: (x - 6)(x + 5) = 0, giving x = 6 or x = -5. With the restriction x ≥ 0, discard x = -5. So the valid root in this case is x = 6.

Case 2: x < 0.
Then |x| = -x and the equation becomes x² + x - 30 = 0. Factor: (x + 6)(x - 5) = 0, giving x = -6 or x = 5. With the restriction x < 0, discard x = 5. So the valid root in this case is x = -6.

Therefore the solutions to the original equation are x = 6 and x = -6.

Check the options:

• (a) x - 6 = 0 → x = 6 (valid)
• (b) x + 6 = 0 → x = -6 (valid)
• (c) x + 5 = 0 → x = -5 (not a solution of the original equation)
• (d) x + 7 = 0 → x = -7 (not a solution of the original equation)

Conclusion: Options (c) and (d) are incorrect, so the correct choice is (E) Both (c) and (d).