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JEE • Mathematics

Quadratic Equation

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Quadratic Equation, Formula and Roots

The source begins with the standard quadratic equation, discriminant, and root relations.

ax2+bx+c=0, a≠0ax^2+bx+c=0,\ a\ne0
x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
D≡b2−4acD\equiv b^2-4ac
α+β=−ba,αβ=ca\alpha+\beta=-\frac{b}{a},\quad \alpha\beta=\frac{c}{a}
(x−α)(x−β)=0⇒x2−(α+β)x+αβ=0(x-\alpha)(x-\beta)=0\Rightarrow x^2-(\alpha+\beta)x+\alpha\beta=0

Variables & Notation

α\alpha

angle or root

β\beta

angle or root

Notes

  • DD is called the discriminant of the quadratic equation.