Solving Quadratics Through The Quadratic Formula Calculator

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The Solving Quadratics Through The Quadratic Formula Calculator will calculate:

1. Calculate the root(s) of the quadratic equation ax² + bx + c = 0 by using the quadratic formula.

Solving Quadratics Through The Quadratic Formula Calculator Parameters: The discriminant must not be negative.

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each solving quadratics through the quadratic formula calculation, the Solving Quadratics Through The Quadratic Formula Calculator will automatically calculate the results and update the formula elements with each element of the solving quadratics through the quadratic formula calculation. You can then email or print this solving quadratics through the quadratic formula calculation as required for later use.

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Related Fields with Tutorials

1. Engineering
2. Physics

Theoretical description

A quadratic equation is a second-order equation with one variable of the form

where x is the variable, a and b are coefficients and c is a constant.

For example, the equation 5x² - 7x + 2 = 0 is a quadratic equation, where a = 5, b = -7 and c = 2.

A quadratic equation may have one or two roots or it may not have any root. The number of roots depends on the sign of the discriminant Δ, which is a mathematical sentence obtained by the equation

Thus,

When the discriminant is positive (Δ > 0) the quadratic equation has two distinct roots:

x₁ = -b - √∆/2a and x₂ = -b + √∆/2a

The joint form of the above formulas is called the quadratic formula, i.e.

When the discriminant is zero (Δ = 0), the quadratic equation has two equal roots (practically, it has a single root):

When the discriminant is negative (Δ < 0), the quadratic equation has no real roots because it is impossible to find the square root of a negative number.