function solveQuadraticEquation() {
var a = parseFloat(document.getElementById('coeffA').value);
var b = parseFloat(document.getElementById('coeffB').value);
var c = parseFloat(document.getElementById('coeffC').value);
var resultDiv = document.getElementById('mathResult');
resultDiv.style.display = "block";
resultDiv.innerHTML = "";
if (isNaN(a) || isNaN(b) || isNaN(c)) {
resultDiv.className = "error";
resultDiv.innerHTML = "Error: Please enter valid numbers for all coefficients.";
return;
}
if (a === 0) {
if (b === 0) {
resultDiv.className = "error";
resultDiv.innerHTML = "Error: Not a valid equation (a and b cannot both be zero).";
} else {
var x = -c / b;
resultDiv.className = "success";
resultDiv.innerHTML = "Linear Equation Result:Since a = 0, this is a linear equation.x = " + x.toFixed(4);
}
return;
}
var discriminant = (b * b) – (4 * a * c);
var x1, x2;
resultDiv.className = "success";
var output = "Discriminant (Δ): " + discriminant.toFixed(4) + "";
if (discriminant > 0) {
x1 = (-b + Math.sqrt(discriminant)) / (2 * a);
x2 = (-b – Math.sqrt(discriminant)) / (2 * a);
output += "Two Real Roots:";
output += "x₁ = " + x1.toFixed(4) + "";
output += "x₂ = " + x2.toFixed(4);
} else if (discriminant === 0) {
x1 = -b / (2 * a);
output += "One Real Root (Repeated):";
output += "x = " + x1.toFixed(4);
} else {
var realPart = (-b / (2 * a)).toFixed(4);
var imagPart = (Math.sqrt(-discriminant) / (2 * a)).toFixed(4);
output += "Two Complex Roots:";
output += "x₁ = " + realPart + " + " + imagPart + "i";
output += "x₂ = " + realPart + " – " + imagPart + "i";
}
resultDiv.innerHTML = output;
}
How to Use the Quadratic Math Problem Solver
Solving quadratic equations is a fundamental skill in algebra. A quadratic equation is any equation that can be rearranged in standard form as ax² + bx + c = 0, where x represents an unknown, and a, b, and c represent known numbers, with a not equal to zero.
Understanding the Quadratic Formula
To find the value of x, we use the quadratic formula:
x = [-b ± √(b² – 4ac)] / 2a
The Role of the Discriminant
The term inside the square root, b² – 4ac, is known as the discriminant (Δ). It tells us the nature of the roots:
If Δ > 0: There are two distinct real roots. The parabola crosses the x-axis at two points.
If Δ = 0: There is exactly one real root (a repeated root). The parabola touches the x-axis at one point.
If Δ < 0: There are no real roots. The roots are complex numbers (involving 'i'), and the parabola does not cross the x-axis.
Find the roots: x₁ = (5 + 1)/2 = 3 and x₂ = (5 – 1)/2 = 2.
Why Use Our Math Problem Solver?
Manual calculation of quadratic equations can lead to simple arithmetic errors, especially when dealing with negative coefficients or complex roots. Our tool provides:
Instant Accuracy: Get precise results for real and complex roots.
Discriminant Calculation: Understand the nature of your equation immediately.
Handles Complex Numbers: Unlike basic calculators, we provide the imaginary (i) components for negative discriminants.
Common Use Cases
Quadratic equations appear in various fields, including physics (calculating projectile motion), economics (finding break-even points), and engineering (designing curved structures like bridges). Whether you are a student checking homework or a professional solving a design problem, our solver ensures your math is correct.