###### Answer: tan(30)=5/b

A quadratic equation with real or complex coefficients has two solutions called roots. These two solutions may or may not be distinct and they may or may not be real. It may be possible to express a quadratic equation ax + bx + c = 0 as a product (px + q)(rx + s) = 0. In some cases it is possible by simple inspection to determine values of p q r and s that make the two forms equivalent to one another. If the quadratic equation is written in the second form then the “Zero Factor Property” states that the quadratic equation is satisfied if px + q = 0 or rx + s = 0. Solvin…

A quadratic equation with real or complex coefficients has two solutions called roots. These two solutions may or may not be distinct and they may or may not be real. It may be possible to express a quadratic equation ax + bx + c = 0 as a product (px + q)(rx + s) = 0. In some cases it is possible by simple inspection to determine values of p q r and s that make the two forms equivalent to one another. If the quadratic equation is written in the second form then the “Zero Factor Property” states that the quadratic equation is satisfied if px + q = 0 or rx + s = 0. Solving these two linear equations provides the roots of the quadratic. For most students factoring by inspection is the first method of solving quadratic equations to which they are exposed. If one is given a quadratic equation in the form x + bx + c = 0 the sought factorization has the form (x + q)(x + s) and one has to find two numbers q and s that add up to b and whose product is c (this is sometimes called “Vieta’s rule” and is related to Vieta’s formulas). As an example x + 5x + 6 factors as (x + 3)(x + 2). The more general case where a does not equal 1 can require a considerable effort in trial and error guess-and-check assuming that it can be factored at all by inspection. Except for special cases such as where b = 0 or c = 0 factoring by inspection only works for quadratic equations that have rational roots. This means that the great majority of quadratic equations that arise in practical applications cannot be solved by factoring by inspection. The process of completing the square makes use of the algebraic identity ${\displaystyle x^{2}+2hx+h^{2}=(x+h)^{2} }$ which represents a well-defined algorithm that can be used to solve any quadratic equation. Starting with a quadratic equation in standard form ax + bx + c = 0

A game based on the algebra with binary variables can be visualized in many different ways. One generic way is to represent the right side of an equation as a clue in a cell (clue cell) and the neighbors of a clue cell as variables. A simple case is shown in Figure 1. The neighbors can be assumed to be the up/down left/right and corner cells that are sharing an edge or a corner. The white cells may contain a hidden object or nothing. In other words they are the binary variables. They take place on the left side of the e…

Quadratic equation – Wikipedia

Quadratic equation – Wikipedia

Quadratic equation – W…