Quadratic Equation

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quadratic equation

[kwä′drad·ik i′kwā·zhən]
(mathematics)
Any second-degree polynomial equation.

Quadratic Equation

 

an equation of the form ax2 + bx + c = 0, where a, b, and c are any number and are called the coefficients of the equation. A quadratic equation has two roots, which are found by the formulas

The expression D = b2 − 4ac is called the discriminant of the quadratic equation. If D > 0, then the roots of the quadratic equation are real and unequal; if D < 0, then the roots areconjugate complex numbers; if D = 0, then the roots are real andequal. The Vièta formulas x1 + x2 = − b/a and x\x2 = c/a link the roots and coefficients of a quadratic equation. The left-hand side of a quadratic equation can be expressed in the form α (xx2) (xx2). The function y = ax2 + bx + c is called a quadratic trinomial, and its graph is a parabola with the vertex at the point M (−b/2a; cb2/4a) and axis of symmetry parallel to the. y-axis; the direction of the branches of the parabola coincides with the sign of a. The solution of the quadratic equation was already known in geometric form to ancient mathematicians.

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The overall correlation between the two data sets was graphically evident, and was confirmed by the numerical correlation between the two data sets, calculated by using JMP, and fitting the data points with a straight line in red, and a second degree polynomial in green (figure 9b); the goodness of fit, expressed by the RSquare parameters listed in the table in figure 9b, was 0.93 and 0.98 for straight line and polynomial, respectively.