Question

Verify whether the following are roots of the polynomial equation indicated against them:

$x^2 - 5 x + 6 = 0;$ $x = 2, 3$

Answer 1

given ⇒ x² - 5x + 6 = 0 
⇒x² -2x -3x + 6 = 0
⇒x(x - 2) - 3(x - 2) = 0
⇒ (x - 2)(x - 3)= 0

so 
when                                           &                    when 
x - 2 = 0 ⇒x = 2                                               x - 3 = 0 ⇒x  = 3 
so verified the following are roots of the polynomial equation

Answer 2

Substitute x=2
2² -5(2)+6
4-10+6 
0
hence x-2 is a root
substitute x=3
3² -5(3)+6
9-15+6
0
hence x-3 is also a root.