Quadratic Equation with One Zero Calculator
Introduction & Importance
Quadratic equations with one zero are a special type of quadratic equation where one of the roots is zero. Understanding and solving these equations is crucial in various fields, including physics, engineering, and economics.
How to Use This Calculator
- Enter the coefficients a, b, and c of your quadratic equation in the respective input fields.
- Click the “Calculate” button.
- View the results below the calculator.
Formula & Methodology
The formula for a quadratic equation is ax² + bx + c = 0. If one root is zero, the equation can be factored as a(x – r)(x – 0) = 0, where r is the non-zero root.
Real-World Examples
Example 1: Physics – Projectile Motion
In physics, the height of a projectile can be modeled by the equation -16t² + vt + h = 0, where t is time, v is the initial velocity, and h is the initial height. If the projectile hits the ground (h = 0), the equation becomes -16t² + vt = 0, a quadratic equation with one zero.
Data & Statistics
| Equation Type | Number of Real Roots | Discriminant |
|---|---|---|
| General Quadratic | 0, 1, or 2 | b² – 4ac |
| Quadratic with One Zero | 1 | b² |
Expert Tips
- To find the non-zero root, use the formula r = b / a.
- If the coefficient a is negative, the parabola opens downwards, and the non-zero root is positive.
- If the coefficient a is positive, the parabola opens upwards, and the non-zero root is negative.
Interactive FAQ
What is the discriminant of a quadratic equation with one zero?
The discriminant is b². Since one root is zero, the other root is b / a.
Can a quadratic equation with one zero have complex roots?
No, since one root is always zero, the other root must be real.