# What is the solution set for #x^2 - 5x + 6 = 0#?

##### 1 Answer

Aug 31, 2015

#### Explanation:

For a general form quadratic equation

#color(blue)(ax^2 + bx + c = 0)#

you can determine its roots by using the *quadratic formula*

#color(blue)(x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a))#

In your case,

#x_(1,2) = (-(-5) +- sqrt((-5)^2 - 4 * 1 * 6))/(2 * 1)#

#x_(1,2) = (5 +- sqrt(1))/2#

#x_(1,2) = (5 +- 1)/2#

The two roots will thus be

#x_1 = (5+1)/2 = color(green)(3)" "# and#" "x_2 = (5-1)/2 = color(green)(2)#