“quadratic equation”的概念、定义、翻译、参考文献-科学参考

quadratic equation

Physics

An equation of the second degree having the form ax²+bx+c=0. Its roots are:

$x = [- b \pm \sqrt (b^{2} - 4 a c)] / 2 a .$

Mathematics

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

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a},$

which is established by completing the square. The term b² − 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 ax² + 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.

Chemical Engineering

A type of polynomial equation in which the highest power of the unknown variable is two, such as x². It has the general form:
$a x^{2} + b x + c = 0$

where a, b, and c are constants. The two roots of the equation can be obtained using the formula:
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

单词	quadratic equation
释义	quadratic equation Physics An equation of the second degree having the form ax²+bx+c=0. Its roots are: $x = [- b \pm \sqrt (b^{2} - 4 a c)] / 2 a .$ Mathematics 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 $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a},$ which is established by completing the square. The term b² − 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 ax² + 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. Chemical Engineering A type of polynomial equation in which the highest power of the unknown variable is two, such as x². It has the general form: $a x^{2} + b x + c = 0$ where a, b, and c are constants. The two roots of the equation can be obtained using the formula: $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
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