The Road to Reality Study Notes: Difference between revisions
→3.2 The real number system
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:With A non-zero, the solutions being (derived from the quadratic formula): | :With A non-zero, the solutions being (derived from the quadratic formula): | ||
:<math>-\frac{B}{2A}\sqrt{(\frac{B}{2A})^2}+\frac{C}{A} | :<math>-\frac{B}{2A}\sqrt{\left(\frac{B}{2A}\right)^2}+\frac{C}{A}, \quad -\frac{B}{2A}\sqrt{\left(\frac{B}{2A}\right)^2}-\frac{C}{A}</math> | ||
:where, to keep within the realm of real numbers, be must have B2 greater than 4AC. When A, B, and C are integers or rational numbers, and where there is no rational solution to the equation, the solutions are quadratic irrationals. | :where, to keep within the realm of real numbers, be must have B2 greater than 4AC. When A, B, and C are integers or rational numbers, and where there is no rational solution to the equation, the solutions are quadratic irrationals. | ||