TI-84 Plus Quadratic Equation Solver
Results:
Enter coefficients and click 'Calculate Roots' to find the solutions for Ax² + Bx + C = 0.
Error:
Please enter valid numbers for all coefficients."; return; } if (a === 0) { if (b === 0) { if (c === 0) { resultDiv.innerHTML = "Results:
Infinite solutions (0 = 0)."; } else { resultDiv.innerHTML = "Results:
No solution (e.g., 5 = 0 is false)."; } } else { // Linear equation: Bx + C = 0 => x = -C/B var x = -c / b; resultDiv.innerHTML = "Results (Linear Equation):
Since A = 0, this is a linear equation.x = " + x.toFixed(4) + ""; } return; } var discriminant = b * b – 4 * a * c; var output = "Results:
"; if (discriminant > 0) { var x1 = (-b + Math.sqrt(discriminant)) / (2 * a); var x2 = (-b – Math.sqrt(discriminant)) / (2 * a); output += "Two distinct real roots:"; output += "x₁ = " + x1.toFixed(4) + ""; output += "x₂ = " + x2.toFixed(4) + ""; } else if (discriminant === 0) { var x = -b / (2 * a); output += "One real root (repeated):"; output += "x = " + x.toFixed(4) + ""; } else { var realPart = -b / (2 * a); var imaginaryPart = Math.sqrt(Math.abs(discriminant)) / (2 * a); output += "Two complex conjugate roots:"; output += "x₁ = " + realPart.toFixed(4) + " + " + imaginaryPart.toFixed(4) + "i"; output += "x₂ = " + realPart.toFixed(4) + " – " + imaginaryPart.toFixed(4) + "i"; } resultDiv.innerHTML = output; }Mastering Quadratic Equations with Your Online TI-84 Plus Solver
The TI-84 Plus graphing calculator has long been an indispensable tool for students and professionals navigating the complexities of mathematics. Known for its versatility, it excels in everything from basic arithmetic to advanced calculus, statistics, and algebra. Among its most frequently used functions is the ability to solve equations, particularly quadratic equations, which are fundamental in various scientific and engineering disciplines.
What is a Quadratic Equation?
A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term in which the unknown variable is raised to the power of two. The standard form of a quadratic equation is:
Ax² + Bx + C = 0
Where:
A,B, andCare coefficients (constants), withAnot equal to zero.xrepresents the unknown variable.
Solving a quadratic equation means finding the values of x that satisfy the equation. These values are often called the "roots" or "solutions" of the equation.
The Quadratic Formula and the Discriminant
While the TI-84 Plus can solve these equations numerically or graphically, the underlying mathematical principle is the quadratic formula:
x = [-B ± √(B² – 4AC)] / 2A
A crucial part of this formula is the term under the square root, known as the discriminant (Δ):
Δ = B² – 4AC
The value of the discriminant tells us about the nature of the roots:
- If Δ > 0: There are two distinct real roots.
- If Δ = 0: There is exactly one real root (a repeated root).
- If Δ < 0: There are two complex conjugate roots.
How Our Online TI-84 Plus Quadratic Solver Works
Our online calculator emulates the equation-solving capabilities of a TI-84 Plus for quadratic equations. Instead of navigating menus on a physical calculator, you simply input the coefficients A, B, and C directly. The calculator then applies the quadratic formula to determine the roots and displays them instantly.
Using the Calculator: Step-by-Step
- Identify Coefficients: For your equation (e.g., 2x² + 3x – 5 = 0), identify A, B, and C. Here, A=2, B=3, C=-5.
- Enter Values: Input the numerical values for 'Coefficient A', 'Coefficient B', and 'Coefficient C' into the respective fields above.
- Calculate: Click the 'Calculate Roots' button.
- View Results: The calculator will display the roots of the equation, indicating whether they are real or complex.
Examples of Quadratic Equation Solving
Let's look at some examples using the calculator:
Example 1: Two Distinct Real Roots
Consider the equation: x² – 5x + 6 = 0
- Coefficient A: 1
- Coefficient B: -5
- Coefficient C: 6
Inputting these values into the calculator will yield:
x₁ = 3.0000
x₂ = 2.0000
Here, the discriminant ((-5)² – 4*1*6 = 25 – 24 = 1) is positive, indicating two distinct real roots.
Example 2: One Real Root (Repeated)
Consider the equation: x² + 4x + 4 = 0
- Coefficient A: 1
- Coefficient B: 4
- Coefficient C: 4
Inputting these values into the calculator will yield:
x = -2.0000
In this case, the discriminant (4² – 4*1*4 = 16 – 16 = 0) is zero, resulting in one repeated real root.
Example 3: Two Complex Conjugate Roots
Consider the equation: x² + 2x + 5 = 0
- Coefficient A: 1
- Coefficient B: 2
- Coefficient C: 5
Inputting these values into the calculator will yield:
x₁ = -1.0000 + 2.0000i
x₂ = -1.0000 – 2.0000i
Here, the discriminant (2² – 4*1*5 = 4 – 20 = -16) is negative, leading to two complex conjugate roots.
This online TI-84 Plus Quadratic Equation Solver provides a quick and accurate way to find the roots of any quadratic equation, mirroring the functionality you'd expect from a physical graphing calculator, but with the convenience of an online tool.