Quadratic equation
A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots. When there is only one distinct root, it can be interpreted as two roots with the same value, called a double root. When there are no real roots, the coefficients can be considered as complex numbers with zero imaginary part, and the quadratic equation still has two complex-valued roots, complex conjugates of each-other with a non-zero imaginary part. A quadratic equation whose coefficients are arbitrary complex numbers always has two complex-valued roots which may or may not be distinct.
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Quotes
[edit]- O! tender girl, out of the swans in a certain lake, ten times the square root of their number went away to Manasarovara when the rainy season arrived, one eighth of that number went away to the Sthala Padmini forest. Three pairs of swans remained in the tank, sporting in the water. What is the total number of swans?
- Mahavira, as quoted in C. K. Raju, Cultural Foundations of Mathematics, Vol. 10, Pt. 4: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe (India: Pearson Longman, 2007)
- A Quadratic equation with solution x=144.
