Quadratic Equation

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quadratic equation

[kwä′drad·ik i′kwā·zhən]
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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Speed matters when the quadratic equation is part of a larger problem.
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It can find that the time and memory needed to solve such equations using Gr[delta]bner bases is essentially the same that is needed to solve the quadratic equations from HS-Sign.
Estimate the probability that the quadratic equations represented by points in a 10,000 by 10,000 region of the coefficient space have real zeros?
Period 1, the quadratic equations ballet; period 2 remaking the Bayeux Tapestry; 3 and 4 double dancing about politics; period 5 science as seen through the prism of a Jimi Hendrix solo.