Answer to Question #250546 in Calculus for bri

Question

Discuss the circumstances under which the x-intercepts of the graph of a quadratic function are included in the solution set of a quadratic inequality and when they are not included.

Answer 1

quadric inequality is inequality which take the next form:

$ax^{2} + bx+c\lor 0$, where $a \not = 0$, $b\in R$, $c\in R$ , $\lor -$ sign of inequality(>, ≥, <, ≤)

f(x) = $ax^{2} + bx+c$

The x-coordinates of the x-intercepts of the graph of f(x) interprets the values of x which converts value of f(x) into 0. So, if the graph has x-intercepts, those x-intercepts should be included in the solution of inequality if the sign of inequality allows f(x) = 0(these signs is ≥ and ≤)

In other case f(x) $\not =$ 0, then x-interceprs should not be included in the solution(if signs is > or <)