Chapter 3, Problem 8CT

Solve, $x^2-10x+24\ge 0$.

To determine

To calculate: The solution of $x^2-10x+24\ge 0$

Answer to Problem 8CT

Solution:

$(-\infty ,4)\cup (6,\infty )$

Explanation of Solution

Given:

The given equation is $x^2-10x+24\ge 0$

Formula used:

We can solve a quadratic inequality $f(x)>0$, and then we have to graph the function $f(x)=0$ and then from the graph find where the function is greater than 0.

The same procedure is applicable for all the other inequalities.

Calculation:

The graph of the function $x^2-10x+24=0$ is

Now, from the graph, we can see that the function is greater than 0 in the interval $(-\infty ,4)\cup (6,\infty )$