Solves any quadratic equation of the form ax² + bx + c = 0
x = (-b ± √(b² - 4ac)) / (2a)
Coefficient of x²
Coefficient of x
Constant term
Unknown variable (solution)
Solve x² + 5x + 6 = 0
Identify: a=1, b=5, c=6
Calculate discriminant: b² - 4ac = 25 - 24 = 1
Apply formula: x = (-5 ± √1) / 2
x = (-5 + 1)/2 = -2 or x = (-5 - 1)/2 = -3
Solve 2x² - 7x + 3 = 0
Identify: a=2, b=-7, c=3
Calculate discriminant: 49 - 24 = 25
Apply formula: x = (7 ± 5) / 4
x = 12/4 = 3 or x = 2/4 = 0.5
The quadratic formula was known to ancient Babylonians around 2000 BC. The modern algebraic form was developed by Arab mathematicians in the 9th century.
Calculating projectile trajectory in physics
Optimizing profit and cost functions in economics
Determining antenna parabola dimensions in engineering
Calculating maximum height of thrown objects
Problem 1: Solve x² + 3x - 10 = 0
Answer: x = 2 or x = -5
Problem 2: Solve 3x² + 8x - 3 = 0
Answer: x = 1/3 or x = -3
Problem 3: Solve x² - 6x + 9 = 0
Answer: x = 3 (double root)
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