Solving $x^2 - 16 x+55> 0$ for $x$

Question

Solving $x^2 - 16 x+55> 0$ for $x$

my work

$$(x-11)(x-5) > 0$$

then x >11 and x > 5

is that correct ???

Answer 1

Draw out the parabola $y=x^2-16x+55$ , using a graphics calculator

We can clearly see that when $x>11$ and $x<5$ the inequality is satisfied.

Answer 2

Yes, the first part of your argument is right

But Carefully introspect the case that 2 negative numbers when multiplied also gives a positive number number

I recommend using the wavy curve method to check your solution to the above inequality

$\quad x\quad \in \quad (-\infty ,5)\cup (11,\infty )$

Answer 3

The equation $f(x)=x^2-16x+55=0$ gives $x=5$ and $x=11$ as the points where the curve cuts the $X-$ axis. Now, it just remains to check the sign of $f(x)$ in the intervals $x<5$, $5<x<11$ and $x>11$. Can you proceed from here?