AP EAMCET · Maths · Quadratic Equation
The number of distinct real solutions for the equation \(\left|x^2+2 x-8\right|+x-2=0\) is
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
\( \left|x^2+2 x-8\right| = 2-x \) \( x \le 2 \) \( |(x+4)(x-2)| = 2-x \) Case A: \( (x+4)(x-2) = 2-x \), when \( (x+4)(x-2) \ge 0 \) (i.e., \( x \le -4 \) or \( x \ge 2 \)) \( (x+4)(x-2) = -(x-2) \) \( (x-2)(x+5) = 0 \) \( x=2, x=-5 \) Both \( x=2 \) and \( x=-5 \) satisfy…
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