0For example, in the quadratic equation \[3x^2-5x-2=0\]:
- \[x\] is the variable, which represents a number whose value we don't know yet.
- The \[^2\] is the power or exponent. An exponent of \[2\] means the variable is .
- \[3\] and \[-5\] are the coefficients, or constant multiples of \[x^2\] and \[x\]. \[3x^2\] is a single , as is \[-5x\].
- \[-2\] is a constant term.
- Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
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The roots of a quadratic equation are usually represented to by the symbols alpha (α), and beta (β). Here we shall learn more about how to find the nature of roots of a quadratic equation without actually finding the roots of the equation.
The nature of roots of a quadratic equation can be found without actually finding the roots (α, β) of the equation. This is possible by taking the discriminant value, which is part of the formula to solve the quadratic equation. The value b2 - 4ac is called the discriminant of a quadratic equation and is designated as 'D'. Based on the discriminant value the nature of the roots of the quadratic equation can be predicted.
