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The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...
A similar but more complicated method works for cubic equations, which have three resolvents and a quadratic equation (the "resolving polynomial") relating and , which one can solve by the quadratic equation, and similarly for a quartic equation (degree 4), whose resolving polynomial is a cubic, which can in turn be solved. [14]
[4] [5] Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation contains only powers of x that are non-negative integers, and therefore it is a polynomial equation. In particular, it is a second-degree polynomial equation, since the greatest power is two.
In general, a quadratic equation can be expressed in the form + + =, [42] where a is not zero (if it were zero, then the equation would not be quadratic but linear). Because of this a quadratic equation must contain the term a x 2 {\displaystyle ax^{2}} , which is known as the quadratic term.
Given a quadratic polynomial of the form + the numbers h and k may be interpreted as the Cartesian coordinates of the vertex (or stationary point) of the parabola. That is, h is the x -coordinate of the axis of symmetry (i.e. the axis of symmetry has equation x = h ), and k is the minimum value (or maximum value, if a < 0) of the quadratic ...
2.1 Mathematics. 2.2 Physics. ... Download as PDF; Printable version; In other projects ... Polynomial equation. Linear equation; Quadratic equation;
We know that one root of this equation is x 1 = A. By standard properties of quadratic equations, we know that the other root satisfies x 2 = kB – A and x 2 = B 2 – k / A . The first expression for x 2 shows that x 2 is an integer, while the second expression implies that x 2 ≠ 0 since k is not a perfect square.
Additional Mathematics is a qualification in mathematics, commonly taken by students in high-school (or GCSE exam takers in the United Kingdom). It features a range of problems set out in a different format and wider content to the standard Mathematics at the same level.
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