Find the number of real solutions for the equation x² - 5|x| + 6 = 0.
Model Answer & Options
Source: Extra Practice4
2
0
3
Explanation
Since x² is same as |x|², we can rewrite the equation as |x|² - 5|x| + 6 = 0. Let y = |x|. Then y² - 5y + 6 = 0. Factoring gives (y - 2)(y - 3) = 0, so y = 2 or y = 3. Since y = |x|, we have |x| = 2 (which gives x = ±2) and |x| = 3 (which gives x = ±3). Total 4 real solutions: {2, -2, 3, -3}. Option B is wrong as it ignores negative roots. Option C and D are incorrect.
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