Single Root Calculator

A single root of a quadratic equation is the value of x that makes the equation equal to zero. This calculator helps you find the single root when the quadratic equation has exactly one real solution.

What is a Single Root?

A single root occurs in quadratic equations when the discriminant is zero. This means the quadratic equation touches the x-axis at exactly one point, forming a "vertex" on the graph.

Quadratic equations are typically written in the form:

ax² + bx + c = 0

Where a, b, and c are coefficients. When the discriminant (b² - 4ac) equals zero, there's exactly one real root.

How to Find a Single Root

To find the single root of a quadratic equation:

Identify the coefficients a, b, and c in the equation ax² + bx + c = 0
Calculate the discriminant using the formula b² - 4ac
If the discriminant equals zero, there's exactly one real root
Use the quadratic formula to find the root: x = -b / (2a)

This method works only when the quadratic equation has exactly one real solution.

Formula

The formula for finding the single root of a quadratic equation is:

x = -b / (2a)

Where:

x is the single root
a is the coefficient of x²
b is the coefficient of x

This formula applies only when the discriminant (b² - 4ac) equals zero.

Example Calculation

Let's find the single root of the equation 2x² + 4x + 2 = 0.

Identify coefficients: a = 2, b = 4, c = 2
Calculate discriminant: (4)² - 4(2)(2) = 16 - 16 = 0
Since discriminant = 0, there's one real root
Apply formula: x = -4 / (2*2) = -4 / 4 = -1

The single root is x = -1.

FAQ

What does a single root mean?: A single root means the quadratic equation touches the x-axis at exactly one point, forming a vertex on the graph.
How do I know if a quadratic has a single root?: Check if the discriminant (b² - 4ac) equals zero. If it does, there's exactly one real root.
Can a quadratic equation have more than one root?: Yes, if the discriminant is positive, there are two distinct real roots. If negative, there are no real roots.
What if the coefficient a is zero?: If a = 0, the equation becomes linear (bx + c = 0) and has exactly one root: x = -c/b.
How is this different from a double root?: A single root and a double root both occur when the discriminant is zero, but a double root has multiplicity 2 in the solution set.