## Quadratic Equations and Inequalities

 2.1 Quadratic Equations and Inequalities

 Definition of Quadratic Equation A quadratic equation in general form can be wirtten as $$ax^2+bx+c=0$$ where $$a$$, $$b$$ and $$c$$ are constants and $$a \neq0$$.

 Quadratic Equation Properties If $$\alpha$$ and $$\beta$$ are the roots of a quadratic equation, then $$(x-\alpha)(x-\beta)=0$$ or $$x^2-(\alpha+\beta)x+\alpha\beta=0$$  For $$x^2-(\alpha+\beta)x+\alpha\beta=0$$,  $$\alpha+\beta$$ is the sum of roots and $$\alpha\beta$$ is the product of roots. For a quadratic equation in the form  $$(x-a)(x-b)=0$$, where $$a \lt b$$, if $$(x-a)(x-b)\gt0$$, then $$x \lt a$$ or $$x \gt b$$. if $$(x-a)(x-b)\lt0$$, then $$a\lt x \lt b$$.

## Quadratic Equations and Inequalities

 2.1 Quadratic Equations and Inequalities

 Definition of Quadratic Equation A quadratic equation in general form can be wirtten as $$ax^2+bx+c=0$$ where $$a$$, $$b$$ and $$c$$ are constants and $$a \neq0$$.

 Quadratic Equation Properties If $$\alpha$$ and $$\beta$$ are the roots of a quadratic equation, then $$(x-\alpha)(x-\beta)=0$$ or $$x^2-(\alpha+\beta)x+\alpha\beta=0$$  For $$x^2-(\alpha+\beta)x+\alpha\beta=0$$,  $$\alpha+\beta$$ is the sum of roots and $$\alpha\beta$$ is the product of roots. For a quadratic equation in the form  $$(x-a)(x-b)=0$$, where $$a \lt b$$, if $$(x-a)(x-b)\gt0$$, then $$x \lt a$$ or $$x \gt b$$. if $$(x-a)(x-b)\lt0$$, then $$a\lt x \lt b$$.