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font-family: 'Arial', sans-serif;
max-width: 700px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ddd;
border-radius: 8px;
background-color: #f9f9f9;
box-shadow: 0 2px 5px rgba(0,0,0,0.1);
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margin-bottom: 20px;
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margin-bottom: 8px;
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TI-89 Quadratic Equation Solver Helper
The TI-89 Titanium graphing calculator is renowned for its powerful symbolic manipulation capabilities, making it an indispensable tool for students and professionals in mathematics, science, and engineering. One of its fundamental uses is solving equations, from simple linear equations to complex polynomial expressions.
This helper focuses on quadratic equations, which are polynomial equations of the second degree, typically written in the form ax² + bx + c = 0. Understanding how to solve these equations is crucial, and the TI-89 can quickly provide exact or approximate solutions, including complex roots.
The general solution for a quadratic equation is given by the quadratic formula:
x = [-b ± sqrt(b² - 4ac)] / 2a
The term (b² - 4ac) is known as the discriminant (often denoted as Δ). The value of the discriminant determines 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 distinct complex conjugate roots.
While the TI-89 can solve these equations with its built-in solve() function or polynomial root finder, this calculator allows you to quickly input the coefficients and see the discriminant and roots calculated, helping you understand the underlying math. It also demonstrates how the TI-89 would handle different scenarios, including linear equations if 'a' is zero.
function calculateQuadraticRoots() {
var coeffA = parseFloat(document.getElementById("coeffA").value);
var coeffB = parseFloat(document.getElementById("coeffB").value);
var coeffC = parseFloat(document.getElementById("coeffC").value);
var errorMessages = document.getElementById("errorMessages");
var equationTypeResult = document.getElementById("equationTypeResult");
var discriminantResult = document.getElementById("discriminantResult");
var root1Result = document.getElementById("root1Result");
var root2Result = document.getElementById("root2Result");
errorMessages.textContent = "";
equationTypeResult.textContent = "";
discriminantResult.textContent = "";
root1Result.textContent = "";
root2Result.textContent = "";
if (isNaN(coeffA) || isNaN(coeffB) || isNaN(coeffC)) {
errorMessages.textContent = "Please enter valid numbers for all coefficients.";
return;
}
if (coeffA === 0) {
// Not a quadratic equation
if (coeffB === 0) {
// Not a linear equation either
if (coeffC === 0) {
equationTypeResult.textContent = "Identity (0 = 0)";
root1Result.textContent = "Infinite solutions";
root2Result.textContent = "";
discriminantResult.textContent = "N/A";
} else {
equationTypeResult.textContent = "Contradiction (C = 0)";
root1Result.textContent = "No solution";
root2Result.textContent = "";
discriminantResult.textContent = "N/A";
}
} else {
// Linear equation: bx + c = 0 => x = -c/b
equationTypeResult.textContent = "Linear Equation";
var x = -coeffC / coeffB;
root1Result.textContent = x.toFixed(4);
root2Result.textContent = "N/A";
discriminantResult.textContent = "N/A";
}
} else {
// Quadratic equation
equationTypeResult.textContent = "Quadratic Equation";
var discriminant = (coeffB * coeffB) – (4 * coeffA * coeffC);
discriminantResult.textContent = discriminant.toFixed(4);
if (discriminant >= 0) {
// Real roots
var root1 = (-coeffB + Math.sqrt(discriminant)) / (2 * coeffA);
var root2 = (-coeffB – Math.sqrt(discriminant)) / (2 * coeffA);
root1Result.textContent = root1.toFixed(4);
root2Result.textContent = root2.toFixed(4);
} else {
// Complex roots
var realPart = -coeffB / (2 * coeffA);
var imaginaryPart = Math.sqrt(Math.abs(discriminant)) / (2 * coeffA);
root1Result.textContent = realPart.toFixed(4) + " + " + imaginaryPart.toFixed(4) + "i";
root2Result.textContent = realPart.toFixed(4) + " – " + imaginaryPart.toFixed(4) + "i";
}
}
}
// Calculate on load with default values
window.onload = calculateQuadraticRoots;