Understanding the Significance of a Positive Discriminant: Two Distinct Real Roots in a Quadratic Equation

If b²-4ac > 0

If b²-4ac > 0, it means that the discriminant of a quadratic equation is positive

If b²-4ac > 0, it means that the discriminant of a quadratic equation is positive. The discriminant is the expression inside the square root of the quadratic formula, given by:
Δ = b² – 4ac

For a quadratic equation in the form of ax² + bx + c = 0, the discriminant determines the nature of the roots. When the discriminant is positive, it indicates that the quadratic equation has two distinct real roots.

This can be seen by substituting the value of the discriminant into the quadratic formula:
x = (-b ± √(b² – 4ac)) / (2a)

When the discriminant is positive, we have:
√(b² – 4ac) > 0

This means that both the numerator and the denominator of the quadratic formula will have real values, and therefore there will be two distinct real roots for the quadratic equation.

As a math tutor, I would explain to you that when the discriminant is positive, it indicates the presence of two distinct real roots for the quadratic equation.

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