Solve ax² + bx + c = 0 Instantly
Solve quadratic equations using the quadratic formula. Our solver provides both real and complex solutions, showing step-by-step work for ax² + bx + c = 0 equations commonly found in algebra and calculus.
Welcome to our Quadratic Equation Solver! Enter the coefficients of your quadratic equation to find the roots and visualize the graph.
A quadratic equation is a second-degree polynomial of the form:
ax² + bx + c = 0
The solutions to this equation are called the roots and can be found using the quadratic formula:
x = [-b ± √(b² - 4ac)] / (2a)
For equations in the form ax² + bx + c = 0, solutions are: x = [-b ± √(b² - 4ac)] / 2a. The discriminant (b² - 4ac) determines the nature of solutions: positive = two real solutions, zero = one real solution (repeated root), negative = two complex conjugate solutions.
Quadratic equations always have two solutions (counting multiplicity). Real solutions represent x-intercepts of the parabola y = ax² + bx + c. Complex solutions occur when the parabola doesn't cross the x-axis. The vertex formula x = -b/2a finds the axis of symmetry.
Quadratic equations appear in: projectile motion problems, optimization in calculus, area and geometry problems, business profit/cost analysis, physics acceleration problems, and engineering design. Mastering quadratic equations is essential for advanced mathematics and sciences.
