Quadratic equation solver
Solved in this tab. Nothing is uploaded.
- Roots
- Two real roots
- x₁
- 1
- x₂
- 2
- Discriminant
- Δ = 1
- Vertex
- (1.5, −0.25)
- Axis of symmetry
- x = 1.5
- y-intercept
- (0, 2)
- Factored form
- (x − 1)(x − 2) = 0
Working
- a = 1, b = −3, c = 2
- Δ = b² − 4ac = (−3)² − 4 × 1 × 2 = 1
- Δ > 0, so there are two real roots.
- x = (−b ± √Δ) / 2a = (3 ± √1) / 2
- x = 1 or 2
Graph
How to use this tool
Solve ax² + bx + c = 0 and see why the answer is right. Nothing is uploaded.
Open Quadratic equation solver
Type a, b and c, or pick an example. Leave b or c empty for 0.
Read the roots
The discriminant tells how many real roots there are. Whole-number coefficients also give the exact answer, and rational roots the factored form.
Check the working and graph
The steps follow the quadratic formula, and the graph marks the vertex and where the parabola crosses the x-axis.
FAQ
How do I solve a quadratic equation?
Write it as ax² + bx + c = 0 and type a, b and c. The roots come from the quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a. The page shows each step.
What does the discriminant tell me?
Δ = b² − 4ac. If it is positive there are two real roots, if it is 0 one repeated root, and if it is negative two complex roots and the parabola does not cross the x-axis.
Why are some answers shown with a square root?
When a, b and c are whole numbers the solver keeps the exact answer, such as (3 ± √5)/2 or 1/2, and gives the decimal next to it. Decimal coefficients get decimal roots.
What are the vertex and the axis of symmetry?
The vertex is the turning point of the parabola, at x = −b ÷ 2a. The axis of symmetry is the vertical line through it. If a is positive the vertex is the lowest point, if negative the highest.
What if a is 0?
Then it is not quadratic: bx + c = 0 is a linear equation with one root, x = −c ÷ b. The page gives that root instead.