For the equation $|x|^2-5|x|+6=0$
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there is only one root
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there are only two distinct roots
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there are only three distinct roots
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there are four distinct roots
Reveal answer
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Correct answer
Explanation
Let y = |x|. The equation becomes y^2 - 5y + 6 = 0, which factors to (y - 2)(y - 3) = 0. Thus, |x| = 2 or |x| = 3. This gives x = 2, -2, 3, -3, resulting in four distinct roots.
AI explanation
Let |x| = y, which changes the equation to y^2 - 5y + 6 = 0. Factoring this quadratic equation gives (y - 2)(y - 3) = 0, meaning y = 2 or y = 3. Replacing y with |x| gives |x| = 2 and |x| = 3, which result in x = 2, x = -2, x = 3, and x = -3. Therefore, the equation has four distinct roots.