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The continued fraction solution to the general monic quadratic equation with complex coefficients x 2 + b x + c = 0 ( b ≠ 0 ) {\displaystyle x^{2}+bx+c=0\qquad (b\neq 0)} given by
Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a continued fraction. Using calculus, e may also be represented as an infinite series, infinite product, or other types of limit of a sequence.
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
The reverse process of expressing a proper rational fraction as the sum of two or more fractions is called resolving it into partial fractions. For example, For example, 2 x x 2 − 1 = 1 x − 1 + 1 x + 1 . {\displaystyle {\frac {2x}{x^{2}-1}}={\frac {1}{x-1}}+{\frac {1}{x+1}}.}
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5.They can be found via the quadratic formula.
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The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
Microsoft’s P/E ratio is a relatively low 33.10 compared to its Magnificent 7 peers, with only Alphabet (Google) and Meta (Facebook) with lower ratios.