The Importance Of Discriminant In Quadratic Equations: Real And Complex Roots

discriminants

if b^2-4ac > 0 then 2 real solutionsif b^2-4ac < 0 then 2 imaginary solutionsif b^2-4ac = 0 then 1 solution with multiplicity of 2

In mathematics, the discriminant is a term used to describe a quantity that is calculated from the coefficients of a polynomial equation. Specifically, the discriminant is the expression found under the square root sign in the quadratic formula, which is used to find the roots of a quadratic equation.

For a quadratic equation Ax² + Bx + C = 0, the discriminant is given by the formula b² – 4ac. It tells us whether the roots of the equation are real or complex, and whether they are distinct or equal. Specifically:

If the discriminant is positive (b² – 4ac > 0), the roots of the equation are real and distinct.

If the discriminant is zero (b² – 4ac = 0), the roots of the equation are real and equal.

If the discriminant is negative (b² – 4ac < 0), the roots of the equation are complex (i.e., involving imaginary numbers, such as the square root of -1). The discriminant can be used to solve problems involving quadratic equations, such as finding the maximum or minimum value of a function or determining the number of solutions to an equation. It is an important concept in algebra and calculus, and is used in many areas of science and engineering.

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