Quadratic Equations and Theory of Equations — Chapter Summary

A quadratic equation is of

A quadratic equation is of the form $ax^2 + bx + c = 0$ where $a \neq 0$. The values of $x$ that satisfy this equation are called its roots. These can

The discriminant $D = b^2

The discriminant $D = b^2 - 4ac$ determines the nature of the roots: if $D > 0$, roots are real and distinct; if $D = 0$, roots are real and equal; if

For a quadratic equation $ax^2 +

For a quadratic equation $ax^2 + bx + c = 0$, the sum of roots $\alpha + \beta = -\frac{b}{a}$ and the product $\alpha\beta = \frac{c}{a}$. These rela

The sign of the expression $ax^2

The sign of the expression $ax^2 + bx + c$ depends on the value of $x$ and the coefficient $a$. If $a > 0$, the parabola opens upwards and has a minim

A polynomial equation of degree $n$

A polynomial equation of degree $n$ has exactly $n$ roots (real or complex). The Factor Theorem states that if $f(\alpha) = 0$, then $(x - \alpha)$ is