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Let α and β be the zeros of the quadratic ax² + bx + c = 0, with β < α < 0. The quadratic equation whose roots are |α| and |β| is:

1. a|x² + |b|x + |c| = 0
2. ax² − |b|x + c = 0
3. a|x² − |b|x + |c| = 0
4. a|x|² + b|x| + |c| = 0

Correct answer: ax² − |b|x + c = 0

Solution

The correct option is right because the roots |α| and |β| are both positive, and the quadratic formed by these roots must maintain the leading coefficient 'a' while adjusting the linear coefficient to account for the absolute value of 'b', which reflects the change in sign of the roots.

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