Unlocking the Power of the Quadratic Formula | Finding Roots and Solutions of Quadratic Equations

quadratic formula

The quadratic formula is a formula used to find the roots or solutions of a quadratic equation

The quadratic formula is a formula used to find the roots or solutions of a quadratic equation. A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.

The quadratic formula is given by:

x = (-b ± √(b^2 – 4ac)) / (2a)

In this formula, ± represents taking both the positive and negative roots, and √ represents the square root. The discriminant, b^2 – 4ac, is used to determine the nature and number of solutions of the quadratic equation.

If the discriminant is positive (b^2 – 4ac > 0), then the equation has two distinct real solutions. These solutions can be found by substituting the values of a, b, and c into the quadratic formula and solving for x.

If the discriminant is zero (b^2 – 4ac = 0), then the equation has one real solution, known as a double root. The value of this solution can be found by substituting the values of a, b, and c into the quadratic formula.

If the discriminant is negative (b^2 – 4ac < 0), then the equation has no real solutions. However, it may have complex solutions, which involve the imaginary unit i (where i^2 = -1). The complex solutions can be obtained by using the quadratic formula and simplifying the expression involving the square root of a negative number. The quadratic formula is a powerful tool in solving quadratic equations, as it provides a systematic way to find their roots. It has applications in various fields such as physics, engineering, and finance, where quadratic equations are commonly encountered.

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