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Quadratic Formula

The quadratic formula is used to solve the quadratic equation:

A quadratic equation can be written as


In the above quadratic equation a, b, and c are constants, and x is the variable which is unknown and is to be found.

The Quadratic Formula is written as quadratic formula

The quadratic formula will deliver two roots for solving any quadratic equation when the equation is solved with both the positive and negative signs in front of the square root one after another.

There will be 3 cases when solving the quadratic equation using the quadratic formula,

if the discriminant $$b^2-4ac$$ is positive, the roots will be real and unequal;

if the discriminant $$b^2-4ac$$ is equal to zero, the two roots will be real and equal to each other;

if the discriminant $$b^2-4ac$$ is negative, the quadratic equation has no real solutions since the square root of the negative number is not a real number. In this case, the roots will be complex and each root is the complex conjugate of the other root.