Whether the discriminant is greater than zero, equal to zero or less than zero can be used to determine if a quadratic equation has no real roots, real and equal roots or real and unequal...

The roots can be equal or unequal, imaginary or real. Learn about the nature of roots using formulas, interactive questions, and illustrations.

Dec 1, 2025 · This concept explores the discriminant and how to use the discriminant to describe the roots and graph of a quadratic function.

2 days ago · If it has real roots, it could either have two distinct real roots or a single repeated root. To distinguish between these three different cases, we have the concept of the discriminant of the …

Nov 16, 2022 · In this section we discuss the solution to homogeneous, linear, second order differential equations, ay'' + by' + c = 0, in which the roots of the characteristic polynomial, ar^2 + br + c = 0, are …

The number of real roots of a quadratic equation is determined by the sign of the discriminant: if the discriminant is positive, there are two real roots; if the discriminant is zero, there is one real root; if …

A non-negative discriminant indicates real roots, while a negative one implies complex roots. By analyzing the sum or product of discriminants, we can infer the possible combinations of roots for a …

By computing the discriminant, it is possible to distinguish whether the quadratic polynomial has two distinct real roots, one repeated real root, or non-real complex roots only.

All the quadratic equations with real roots can be factorized. The physical significance of the roots is that at the roots of an equation, the graph of the equation intersects x-axis. The x-axis represents the real …

The value of the discriminant shows how many roots f(x) has: If b2 – 4ac > 0 then the quadratic function has two distinct real roots. If b2 – 4ac = 0 then the quadratic function has one repeated real root. If …