Mastering The Discriminant Formula: How To Determine The Nature Of Roots For A Quadratic Equation

discriminant formula

b^2-4ac

The discriminant formula is a mathematical formula used to determine the nature or type of roots of a quadratic equation. It is represented as follows:

b² – 4ac

where a, b, and c represent the coefficients of the quadratic equation in the standard form ax² + bx + c = 0.

The discriminant can take on three possible values, each of which indicates the nature of the roots of the quadratic equation:

1. If the discriminant is greater than zero (b² – 4ac > 0), then the quadratic equation has two distinct real roots. This means that the equation crosses the x-axis at two different points.

2. If the discriminant is equal to zero (b² – 4ac = 0), then the quadratic equation has one repeated real root. This means that the equation touches the x-axis at one point.

3. If the discriminant is less than zero (b² – 4ac < 0), then the quadratic equation has two complex roots. This means that the equation does not intersect the x-axis (since complex roots do not lie on the real number line). Instead, the roots represent two imaginary points that lie on the complex plane. In summary, the discriminant formula is a useful tool that allows us to quickly determine the nature of the roots of a quadratic equation.

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