Write the quadratic equation whose roots are calculator

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Quadratic Formula Calculator

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Example: 2x^2-5x-3=0

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2x2−5x−3=0


About the quadratic formula

Solve an equation of the form ax2+bx+c=0 by using the quadratic formula:

x=

−b±√b2−4ac
2a

Quadratic Formula Video Lesson

Write the quadratic equation whose roots are calculator

Solve with the Quadratic Formula Step-by-Step [1:29]

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Step-by-Step Examples

Algebra

Quadratic Equations

Find the Quadratic Equation Given the Roots

Step 1

and are the two real distinct solutions for the quadratic equation, which means that and are the factors of the quadratic equation.

Step 2

Expand using the FOIL Method.

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Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Step 3

Simplify and combine like terms.

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Simplify each term.

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Multiply by .

Move to the left of .

Rewrite as .

Multiply by .

Subtract from .

Step 4

The standard quadratic equation using the given set of solutions is .

Step 5

Enter YOUR Problem

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We can help you solve an equation of the form "ax2 + bx + c = 0"
Just enter the values of a, b and c below:

algebra/images/quadratic-solver.js

Is it Quadratic?

Only if it can be put in the form ax2 + bx + c = 0, and a is not zero.

The name comes from "quad" meaning square, as the variable is squared (in other words x2).

These are all quadratic equations in disguise:

In disguiseIn standard forma, b and c
x2 = 3x -1 x2 - 3x + 1 = 0 a=1, b=-3, c=1
2(x2 - 2x) = 5 2x2 - 4x - 5 = 0 a=2, b=-4, c=-5
x(x-1) = 3 x2 - x - 3 = 0 a=1, b=-1, c=-3
5 + 1/x - 1/x2 = 0 5x2 + x - 1 = 0 a=5, b=1, c=-1

How Does this Work?

The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:

The "±" means we need to do a plus AND a minus, so there are normally TWO solutions !

The blue part (b2 - 4ac) is called the "discriminant", because it can "discriminate" between the possible types of answer:

  • when it is positive, we get two real solutions,
  • when it is zero we get just ONE solution,
  • when it is negative we get complex solutions.

Learn more at Quadratic Equations

Note: you can still access the old version here.

How do you find a quadratic equation whose roots are given?

The formula to find the roots of the quadratic equation is x = [-b ± √(b2 - 4ac)]/2a. The sum of the roots of a quadratic equation is α + β = -b/a. The product of the Root of the quadratic equation is αβ = c/a. The quadratic equation whose roots are α, β, is x2 - (α + β)x + αβ = 0.

Can a calculator do the quadratic formula?

Calculator Use The calculator solution will show work using the quadratic formula to solve the entered equation for real and complex roots. Calculator determines whether the discriminant (b2−4ac) is less than, greater than or equal to 0. When b2−4ac=0 there is one real root. When b2−4ac>0 there are two real roots.

What is the quadratic equation whose roots are A and B?

A quadratic equation, whose roots are α and β can be written as (x−α)(x−β)=0=x2−(α+β)x+αβ