A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. Quadratic equations are typically solved using the quadratic formula, which states that the solutions are given by:
x = (-b ± √(b^2 – 4ac)) / 2a
The ‘±’ sign indicates that there are two possible solutions – one with the plus sign and one with the minus sign. The discriminant, b^2 – 4ac, determines the nature of the solutions:
– If the discriminant is positive, there are two distinct real solutions.
– If the discriminant is zero, there is one real solution (known as a repeated root).
– If the discriminant is negative, there are two complex solutions (conjugate pairs) that involve the imaginary unit, i.
Quadratic equations arise in various areas of mathematics and science, and they are widely used in solving problems involving shapes, motion, optimization, and more.
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