Quadratic Equations and Inequalities
\(\blacksquare\) A quadratic equation in general form can be written as
\(ax^2+bx+c=0\)
where \(a\), \(b\) and \(c\) are constants and \(a \ne 0\).
\(\blacksquare\) Methods used to solve quadratic equations:
2. Formula
\(\boxed{x=\dfrac{-b \pm \sqrt{b^2-4ac}} {2a}}\)
\(\blacksquare\) If \(\alpha\) and \(\beta\) are the roots of a quadratic equation, then
\((x-\alpha)(x-\beta)=0\)
or
\(x^2-(\alpha+\beta)x+\alpha\beta=0\)
\(\blacksquare\) For \(x^2-(\alpha+\beta)x+\alpha\beta=0\),
\(\alpha+\beta\) is the sum of roots and \(\alpha\beta\) is the product of roots.
\(\blacksquare\) For a quadratic equation in the form
\((x-a)(x-b)=0\),
where \(a \lt b\),
Assess yourself by staged practices