Algebra Calculator Free

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Quadratic Algebra Calculator

Solve quadratic equations in the form of ax² + bx + c = 0 instantly.

Solution:

function calculateAlgebraResult() { var a = parseFloat(document.getElementById('coeffA').value); var b = parseFloat(document.getElementById('coeffB').value); var c = parseFloat(document.getElementById('coeffC').value); var resultBox = document.getElementById('algebra-result-display'); var eqDisplay = document.getElementById('equation-display'); var valDisplay = document.getElementById('result-values'); var discDisplay = document.getElementById('discriminant-info'); if (isNaN(a) || isNaN(b) || isNaN(c)) { alert("Please enter valid numbers for coefficients a, b, and c."); return; } resultBox.style.display = 'block'; eqDisplay.innerHTML = "Solving for: " + a + "x² + (" + b + ")x + (" + c + ") = 0"; if (a === 0) { if (b === 0) { valDisplay.innerHTML = c === 0 ? "Infinite solutions (Identity)" : "No solution (Contradiction)"; discDisplay.innerHTML = ""; } else { var linearRoot = -c / b; valDisplay.innerHTML = "Linear Solution: x = " + linearRoot.toFixed(4); discDisplay.innerHTML = "Note: Since a=0, this is a linear equation."; } return; } var discriminant = (b * b) – (4 * a * c); discDisplay.innerHTML = "Discriminant (Δ) = " + discriminant.toFixed(2); if (discriminant > 0) { var x1 = (-b + Math.sqrt(discriminant)) / (2 * a); var x2 = (-b – Math.sqrt(discriminant)) / (2 * a); valDisplay.innerHTML = "Two Real Roots: x₁ = " + x1.toFixed(4) + "x₂ = " + x2.toFixed(4); } else if (discriminant === 0) { var x = -b / (2 * a); valDisplay.innerHTML = "One Real Root (Repeated): x = " + x.toFixed(4); } else { var realPart = (-b / (2 * a)).toFixed(4); var imagPart = (Math.sqrt(-discriminant) / (2 * a)).toFixed(4); valDisplay.innerHTML = "Two Complex Roots: x₁ = " + realPart + " + " + imagPart + "ix₂ = " + realPart + " – " + imagPart + "i"; } }

Mastering Algebra: The Quadratic Equation Guide

Algebra is a cornerstone of mathematics that allows us to find unknown values by balancing equations. One of the most common challenges students and professionals face is solving the quadratic equation. 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.

How This Algebra Calculator Works

This calculator utilizes the Quadratic Formula to find the roots (values of x) for any given quadratic expression. The formula used is:

x = [-b ± √(b² – 4ac)] / 2a

The term inside the square root, b² – 4ac, is known as the Discriminant. It tells us the nature of the roots:

  • Positive Discriminant: Two distinct real number solutions.
  • Zero Discriminant: Exactly one real number solution (a repeated root).
  • Negative Discriminant: Two complex (imaginary) solutions.

Real-World Example

Imagine you are calculating the trajectory of a ball thrown into the air. The height (h) over time (t) might be represented by the equation -5t² + 10t + 2 = 0. To find when the ball hits the ground:

  1. Identify the coefficients: a = -5, b = 10, c = 2.
  2. Input these values into the algebra calculator above.
  3. The calculator will compute the discriminant (10² – 4*(-5)*2 = 140).
  4. It then provides the time values (roots) where the height is zero.

Why Use a Free Algebra Calculator?

While solving by hand is great for learning, an online tool ensures accuracy and saves time, especially when dealing with decimals or complex numbers. This tool is perfect for:

  • Verifying homework assignments.
  • Engineering and physics calculations.
  • Quickly finding the zeros of a function for graphing.
  • Solving equations that are not easily factorable.

Common Algebra Terms to Know

Coefficient: The number multiplied by a variable (like the '5' in 5x²).

Variable: A symbol (usually x or y) representing a number we don't know yet.

Constant: A fixed value, like 'c' in our formula, that does not change.

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