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单词 quadratic equation
释义

quadratic equation

A quadratic equation in the unknown x is an equation of the form ax2 + bx + c = 0, where a, b and c are given real numbers, with a ≠ 0. This may be solved by completing the square or by using the quadratic formula

which is established by completing the square. The term b 2 − 4ac is known as the discriminant. The equation has two distinct real roots, a repeated real root, or two complex conjugate roots, depending on whether the discriminant is positive, zero, or negative respectively.

If α and β are the roots of the quadratic equation ax 2 + bx + c = 0, then α + β = −b/a and αβ = c/a. (See Viète's formulae.) The quadratic formula is still valid over other fields provided that the discriminant has a square root in the field.

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更新时间:2025/4/29 5:05:42