Positive and Negative Real Roots Calculator

What Are Real Roots?

Real roots of an equation are the real numbers that satisfy the equation. For a quadratic equation in the form ax² + bx + c = 0, the roots are the solutions that make the equation true.

Real roots can be positive or negative depending on the values of a, b, and c. Positive roots are greater than zero, while negative roots are less than zero.

How to Find Roots

There are several methods to find the roots of a quadratic equation:

1. Factoring: Express the quadratic as a product of two binomials.
2. Quadratic Formula: Use the formula x = [-b ± √(b² - 4ac)] / (2a).
3. Completing the Square: Rewrite the equation in the form (x + p)² = q.

The quadratic formula is the most reliable method as it works for all quadratic equations.

Positive and Negative Roots

The sign of the roots depends on the coefficients a, b, and c:

• If a, b, and c are all positive, both roots are negative.
• If a and c are positive and b is negative, one root is positive and the other is negative.
• If a is positive and b and c are negative, both roots are positive.

The discriminant (b² - 4ac) determines the nature of the roots:

• Positive discriminant: Two distinct real roots.
• Zero discriminant: One real root (repeated).
• Negative discriminant: No real roots (complex roots).

Example Calculation

Let's solve the equation x² - 5x + 6 = 0:

The roots are 3 and 2, both positive.