Question

find the roots of x² - 9x + 14 > 0 of its corresponding equality?​

Answer 1

x² - 9x + 14 > 0

x² - 7x - 2x + 14 > 0

x(x - 7) - 2(x - 7) > 0

(x - 7)(x - 2) > 0

So, x > 7 and x > 2

Domain x belongs to (7,∞)

Answer 2

Given: $\[{x^2} - 9x + 14 > 0\]$

Solution:

Find the factors of $\[{x^2} - 9x + 14\]$.

$\[\begin{array}{l}{x^2} - 9x + 14\\ \Rightarrow {x^2} - 7x - 2x + 14\\ \Rightarrow x\left( {x - 7} \right) - 2\left( {x - 7} \right)\\ \Rightarrow \left( {x - 2} \right)\left( {x - 7} \right)\end{array}\]$

Understand that,

$\[\begin{array}{l}{x^2} - 9x + 14 > 0\\ \Rightarrow \left( {x - 2} \right)\left( {x - 7} \right) > 0\\ \Rightarrow x - 2 > 0\,\,or\,\,x - 7 > 0\\ \Rightarrow x > 2\,\,or\,\,x > 7\end{array}\]$

Hence, the roots of $\[{x^2} - 9x + 14 > 0\]$ are 2 and 7 respectively.