The Conjugate Roots Theorem Calculator is a powerful tool designed to unravel the secrets hidden within quadratic equations. These equations take the form ax^2 + bx + c = 0, where 'a,' 'b,' and 'c' are coefficients. The calculator provides insights into the roots of these equations, unveiling essential details about their sum and product.
Formula of Conjugate Roots Theorem Calculator
Given quadratic equation: ax^2 + bx + c = 0
- Sum of roots = -b/a
- Product of roots = c/a
If one root is a complex number p + qi, then its conjugate p - qi is also a root.
Root 1 = (-b + sqrt(b^2 - 4ac)) / (2a) Root 2 = (-b - sqrt(b^2 - 4ac)) / (2a)
Where:
- 'a,' 'b,' and 'c' are the coefficients of the quadratic equation ax^2 + bx + c = 0
- sqrt denotes the square root function.
General Terms Table
To assist users in better understanding and utilizing the Conjugate Roots Theorem Calculator, here is a table of general terms commonly associated with quadratic equations:
| Term | Definition |
|---|---|
| Quadratic Equation | A polynomial equation of second degree, ax^2 + bx + c = 0 |
| Coefficients | Numeric factors ('a,' 'b,' and 'c') in the quadratic equation |
| Roots | The values of 'x' that satisfy the quadratic equation |
| Sum of Roots | The arithmetic total of the roots, calculated as -b/a |
| Product of Roots | The result of multiplying the roots, calculated as c/a |
| Complex Number | A number of the form p + qi, where p and q are real numbers |
Example of Conjugate Roots Theorem Calculator
Let's consider a practical example to illustrate the functionality of the Conjugate Roots Calculator.
Given quadratic equation: 2x^2 + 5x + 3 = 0
Using the calculator, we find:
- Sum of roots = -5/2
- Product of roots = 3/2
- Roots: x₁ = -1 and x₂ = -3/2
This example showcases how the calculator efficiently processes quadratic equations, providing valuable insights into their roots.
Most Common FAQs
A: If the roots involve complex numbers (p + qi), the calculator ensures accuracy by considering their conjugates (p - qi).
A: Yes, the Conjugate Roots Calculator works for any quadratic equation in the standard form ax^2 + bx + c = 0.
A: The calculator primarily focuses on solving quadratic equations, making it ideal for mathematics-related tasks.