solve the quadratic inequality. write the solution set in interval notation.

Question

x^2- 9x+ 18> 0

Answer 1

Quadratic inequality is x² - 9x + 18 > 0

Factor it like an equation

x² - 3x - 6x + 18 > 0

x(x - 3) - 6(x - 3) > 0

(x - 3)*(x - 6) > 0

Now product of two numbers can only be positive if both numbers are positive i.e >0 or both the numbers are negative ie. < 0

x - 3 > 0 and x - 6 > 0 => x > 6 ; or

x - 3 < 0 and x - 6 < 0 => x < 3

So answer has to be (- ∞, 3) U ( 6, ∞).