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First Root of Quadratic Equation Formula:
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The First Root of Quadratic Equation is the value of one of the variables satisfying the given quadratic equation f(x), such that f(x1) = 0. It represents one of the two possible solutions to a quadratic equation.
The calculator uses the quadratic formula:
Where:
Explanation: The quadratic formula provides the roots of a quadratic equation of the form ax² + bx + c = 0, where the discriminant determines the nature of the roots.
Details: Finding the roots of quadratic equations is fundamental in algebra and has applications in physics, engineering, economics, and many other fields where relationships between variables need to be analyzed.
Tips: Enter the numerical coefficients b and a, and the discriminant D. Ensure the discriminant is non-negative (D ≥ 0) for real roots, and coefficient a is not zero.
Q1: What if the discriminant is negative?
A: If the discriminant is negative, the quadratic equation has complex roots, which this calculator does not handle.
Q2: Why is coefficient a required to be non-zero?
A: If a = 0, the equation becomes linear, not quadratic, and the quadratic formula does not apply.
Q3: What does the discriminant tell us about the roots?
A: The discriminant indicates the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root (repeated), D < 0 means two complex roots.
Q4: Can this calculator find both roots?
A: This calculator finds only the first root (using the + sign). The second root can be found using x2 = (-b - sqrt(D))/(2a).
Q5: What are some practical applications of quadratic equations?
A: Quadratic equations are used in projectile motion, optimization problems, electrical circuit analysis, and many other real-world scenarios.