Solve any quadratic equation of the form ax² + bx + c = 0. Find both roots, discriminant, and vertex with step-by-step solution.
A Quadratic Equation Calculator solves equations in the standard form ax squared plus bx plus c equals zero, finding the values of x that satisfy the equation.
The quadratic formula states x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a.
Enter the coefficients a, b, and c from your equation. Click Calculate. The tool shows both roots along with whether they are real or complex.
Example 1: For x squared minus 5x plus 6 equals zero, the roots are x equals 2 and x equals 3.
Example 2: For x squared plus 4x plus 4 equals zero, there is one repeated root, x equals negative 2.
Example 3: For x squared plus 1 equals zero, the roots are complex numbers since the discriminant is negative.
Solving algebra homework involving quadratic equations. Calculating projectile motion in physics problems. Finding break even points in business and economics. Determining maximum or minimum values in optimization problems.
What is the discriminant. It is b squared minus 4ac, and it tells you the nature of the roots.
What happens when the discriminant is negative. The equation has two complex roots instead of real number solutions.
Can a equal zero in a quadratic equation. No, if a equals zero the equation becomes linear, not quadratic.
What does a repeated root mean. It means the parabola touches the x axis at exactly one point.
Is there another way to solve quadratics besides the formula. Yes, factoring and completing the square are also common methods.