If b²-4ac > 0
If b² – 4ac is greater than zero, it means that the discriminant is positive
If b² – 4ac is greater than zero, it means that the discriminant is positive. The discriminant is a term used in solving quadratic equations and is calculated by taking the square of the coefficient of the linear term (b) and subtracting four times the product of the coefficient of the quadratic term (a) and the constant term (c).
When the discriminant is positive, it signifies that the quadratic equation has two distinct real solutions. In other words, the quadratic equation crosses or intersects the x-axis at two different points.
Graphically, this would represent a parabola that opens upwards (if a is positive) or downwards (if a is negative) and intersects the x-axis at two distinct points. The equation could be of the form ax² + bx + c = 0, where a, b, and c are constants, and x represents the variable.
In terms of application, a positive discriminant could indicate scenarios such as finding the roots of a quadratic equation, determining the time of flight in projectile motion, or solving optimization problems that involve quadratic functions.
More Answers:
Understanding the Nature of Quadratic Solutions | Discerning Negative Discriminant and Complex Conjugate Solutions.Understanding the Quadratic Equation | The Meaning of b²-4ac=0 and its Implication on Real Roots
Understanding the Discriminant in Quadratic Equations | A Guide to Classifying Solutions