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Equations of the form ax² + bx + c = 0 require the use of a Java quadratic equation program. The discriminant (Δ), which specifies the nature of the roots, is used in this software to calculate the roots using the quadratic formula. When Δ is positive, two real roots are produced; when Δ is zero, one real root is produced; and when Δ is negative, complex roots are produced. It is necessary to define coefficients, compute the discriminant, and identify the roots based on circumstances when writing a Java application for a quadratic equation.
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