Understanding the Discriminant in Quadratic Equations – Real and Complex Roots Explanation

Discriminant

b²-4ac

In mathematics, a discriminant is a term that appears under the square root sign (radical) in the quadratic formula. The quadratic formula is a mathematical formula used to find the roots or solutions of a quadratic equation. The items under the radical sign in the formula are known as the discriminant.

The discriminant represents the nature of the roots of a quadratic equation. It helps to determine if the roots of the equation are real or complex, and if they are real, whether the roots are rational or irrational.

For a quadratic equation of the form ax^2 + bx + c = 0, the discriminant can be calculated using the formula b^2 – 4ac. The value of the discriminant determines the nature of the roots.

If the discriminant is positive, the quadratic equation has two distinct real roots.

If the discriminant is zero, the quadratic equation has one real root, which is a repeated root or a perfect square.

If the discriminant is negative, the quadratic equation has two complex roots.

Knowing the discriminant can be useful in solving quadratic equations and understanding the behavior of quadratic functions.

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