# Quadratic Inequalities

Graph of an equation y = bx + c gives us the straight line and it is termed as the linear equation. But, if we add a term ‘ax^{2}’ to it, the graph changes into a parabola. And, the equation after adding ax^{2} becomes ax^{2} + bx + c and that is known as a Quadratic equation.

Quadratic equation is an equation which is of degree 2 and is of the form ax^{2} + bx + c = 0. Solution of the equation is $x$ = $\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$ where ‘a’, ‘b’ and ‘c’ are the real numbers. Therefore, value of a $\neq$ 0.

3x^{2} + 8x - 9, 4x^{2} – 5x + 16 and x^{2} – 45 are all examples of the quadratic equations.

The values of a, b and c in the equation are termed as the coefficients wherein ‘a’ is the coefficient of x^{2} and b is the coefficient of x and c is usually called as the constant. If we want to compare one quantity with another, we make use of the inequalities symbols. **For example:** 2 < 10.

There are different symbols that we use to express the inequalities, where

> indicates greater than

< indicates less than

$\leq$ indicates less than or equal to

$\geq$ indicates greater than or equal to