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.

References in periodicals archive ?
In summary, while the discriminant is positive but decreasing, the two real solutions of quadratic equations get closer to each other along the real or x-axis until they equal each other (one real solution) when the discriminant equals zero.
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A mind-numbing load of quadratic equations to work through.
They had a general procedure equivalent to solving quadratic equations, although they recognized only one root and that had to be positive.
When an author and a British politician both questioned the teaching of quadratic equations the AAMT email list members responded admirably.
Would this bring back unwelcome memories of afternoons at school attempting to master quadratic equations and long division?
The major topics of school algebra include symbols and expressions, linear equations, quadratic equations, functions, polynomials, and combinatorics and finite probability.