Affected Quadratic Equations.

• x}{x} = \dfrac{29}{10}$.

36. ${\displaystyle \frac{2x-1}{x-1}}+{\displaystyle \frac{1}{6}}={\displaystyle \frac{2x-3}{x-2}}$.

164. Problems involving Quadratics.

Problems which involve quadratic equations apparently have two solutions, since a quadratic equation has two roots.

When both roots of the quadratic equation are positive integers, they will, in general, both be admissible solutions. Fractional and negative roots will in some problems give admissible solutions; in other problems they will not give admissible solutions.

The reason that every root of the equation will not always satisfy the conditions of the problem is that the problem may have certain restrictions, expressed or implied, that cannot be expressed in the equation.

No difficulty will be found in selecting the result which belongs to the particular problem we are solving. Sometimes, by a change in the statement of the problem, we may form a new problem which corresponds to the result that was inapplicable to the original problem.

Here as in simple equations x stands for an unknown number.