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Quadratic Equation

★★☆☆☆Middle School

📖Definition

An equation where the highest power of the variable is 2.

ax² + bx + c = 0 (a ≠ 0)

Standard form of quadratic equation

x = \frac-b ± √b² - 4ac2a

Quadratic formula

D = b² - 4ac

Discriminant: D>0 two real roots, D=0 one root, D<0 complex roots

x₁ + x₂ = -(b)/(a), x₁ x₂ = (c)/(a)

Vieta's formulas

예제 1★★☆☆☆

Solve x² - 5x + 6 = 0.

x² - 5x + 6 = (x-2)(x-3) = 0

예제 2★★★☆☆

Solve 2x² + 3x - 2 = 0 using the quadratic formula.

x = \frac-3 ± √254 = (1)/(2), -2

Babylonians solved quadratic equations as early as 2000 BCE.

Projectile motion, free fall

Profit maximization, cost minimization

#algebra#equation#quadratic#fundamental