All of the equations we have solved so far have had...

All of the equations we have solved so far have had rational-number coefficients. However, the quadratic formula can be used to solve quadratic equations with irrational or even imaginary coefficients.
$100 i x^{2}+300 x-200 i=0$

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Key Concepts

Quadratic Formula

The quadratic formula is a universal method for solving quadratic equations by substituting the coefficients into the expression (-b ± ?(b² - 4ac))/(2a). This formula is powerful because it can yield solutions in cases where the coefficients or the discriminant are irrational or complex, thereby ensuring that every quadratic equation has a calculable solution.

Complex Numbers

Complex numbers extend the real number system to include numbers of the form a + bi, where 'i' is the imaginary unit defined by the property i² = -1. This concept becomes crucial when solving quadratic equations that result in a negative discriminant or contain imaginary coefficients, as it enables the handling of solutions that cannot be represented on the real number line.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation typically expressed in the form ax² + bx + c = 0. These equations serve as a fundamental part of algebra, and their solutions represent points where a parabolic graph intersects the x-axis. The structure of quadratic equations allows for a standardized method of solving them regardless of the types of coefficients involved.

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