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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.

 🖹 Normal View🗖 Full Page View Calculator Precision (Decimal Places)0123456789101112131415 Coefficient (a) Coefficient (b) Constant (c)
First root of the quadratic equation Formula and Calculations First root of the quadratic equation, x1 = Second root of the quadratic equation, x2 = x1 = -b - √b2 - 4ac/2ax1 = - √2 - 4 × × /2 × x1 = - √ - /x1 = - √/x1 = - /x1 = /x1 = x2 = -b + √b2 - 4ac/2ax2 = + √2 - 4 × × /2 × x2 = + √ - /x2 = + √/x2 = + /x2 = /x2 = Coefficient (a) = Coefficient (b) = Constant (c) =

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## Theoretical description

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

y = ax2 + bx + c = 0

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

∆ = b2 - 4ac

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.

x1,2 = -b ∓ √∆/2a

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

x1 = x2 = -b/2a

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.

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