.calculator-container {
background-color: #f9f9f9;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
font-family: Arial, sans-serif;
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.calculator-form label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.calculator-form input[type="number"] {
width: calc(100% – 22px);
padding: 10px;
margin-bottom: 15px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
.calculator-form button {
background-color: #007bff;
color: white;
padding: 12px 20px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
width: 100%;
box-sizing: border-box;
}
.calculator-form button:hover {
background-color: #0056b3;
}
.calculator-result {
margin-top: 20px;
padding: 15px;
border: 1px solid #e0e0e0;
border-radius: 4px;
background-color: #e9ecef;
min-height: 50px;
color: #333;
}
.calculator-result p {
margin: 5px 0;
font-size: 1.1em;
}
.calculator-result b {
color: #0056b3;
}
.calculator-article {
max-width: 600px;
margin: 40px auto;
font-family: Arial, sans-serif;
line-height: 1.6;
color: #333;
}
.calculator-article h3 {
color: #007bff;
margin-top: 30px;
margin-bottom: 15px;
}
.calculator-article p {
margin-bottom: 10px;
}
.calculator-article ul {
list-style-type: disc;
margin-left: 20px;
margin-bottom: 10px;
}
.calculator-article li {
margin-bottom: 5px;
}
Understanding Quadratic Equations
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 'x' represents an unknown, and 'a', 'b', and 'c' are coefficients, with 'a' not equal to zero. If 'a' were zero, the equation would be linear, not quadratic.
The Quadratic Formula
To find the values of 'x' (also known as the roots or solutions) that satisfy a quadratic equation, we use the quadratic formula:
x = [-b ± √(b² – 4ac)] / 2a
The term inside the square root, (b² – 4ac), is called the discriminant (often denoted by Δ). 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 no real roots (two complex conjugate roots).
How to Use This Calculator
This calculator helps you find the real roots of any quadratic equation in the standard form ax² + bx + c = 0. Simply enter the coefficients 'a', 'b', and 'c' into the respective fields and click "Calculate Roots".
- Coefficient 'a': The number multiplying x².
- Coefficient 'b': The number multiplying x.
- Coefficient 'c': The constant term.
The calculator will then display the real solutions for 'x', or inform you if there are no real solutions or if the equation is linear.
Examples
Let's look at a few examples:
Example 1: Two Distinct Real Roots
Equation: x² – 3x + 2 = 0
Using the calculator with these values will yield: x1 = 2, x2 = 1.
Example 2: One Real Root (Repeated)
Equation: x² – 4x + 4 = 0
Using the calculator with these values will yield: x = 2.
Example 3: No Real Roots
Equation: x² + x + 1 = 0
Using the calculator with these values will yield: "No real solutions."
Example 4: Linear Equation (a = 0)
Equation: 0x² + 2x – 4 = 0 (which simplifies to 2x – 4 = 0)
Using the calculator with these values will yield: "This is a linear equation (a=0). The solution is: x = 2."
function calculateQuadratic() {
var a = parseFloat(document.getElementById("coefficientA").value);
var b = parseFloat(document.getElementById("coefficientB").value);
var c = parseFloat(document.getElementById("coefficientC").value);
var resultDiv = document.getElementById("result");
var output = "";
if (isNaN(a) || isNaN(b) || isNaN(c)) {
output = "Please enter valid numbers for all coefficients.";
resultDiv.innerHTML = output;
return;
}
if (a === 0) {
// It's a linear equation: bx + c = 0 => x = -c/b
if (b === 0) {
if (c === 0) {
output = "Infinite solutions (0 = 0).";
} else {
output = "No solution (e.g., 5 = 0).";
}
} else {
var x = -c / b;
output = "This is a linear equation (a=0). The solution is:
";
}
resultDiv.innerHTML = output;
return;
}
var discriminant = b * b – 4 * a * c;
if (discriminant > 0) {
var x1 = (-b + Math.sqrt(discriminant)) / (2 * a);
var x2 = (-b – Math.sqrt(discriminant)) / (2 * a);
output = "There are two distinct real roots:";
output += "
";
} else if (discriminant === 0) {
var x = -b / (2 * a);
output = "There is one real root (repeated):";
output += "
";
} else {
// discriminant < 0, complex solutions
var realPart = (-b / (2 * a)).toFixed(4);
var imaginaryPart = (Math.sqrt(Math.abs(discriminant)) / (2 * a)).toFixed(4);
output = "There are no real roots (complex solutions):";
output += "