Distinguish the discriminant and number of solutions for the equation. Show your work and explain the steps you used to solve. x^2 − 5x + 6 = 0

Answer 1

x^2 -5x +6 = 0

discriminant = b^2 -4ac = 25-24 = 1>0, which means 2 real solutions, 2 intersections with the x axis, 2 roots or zeros.

factor

(x-3)(x-2) = 0

set each factor =0

x-3=0, x-2=0

x =3 or 2

or use the quadratic formula

x = 5/2 + or - (1/2)sqr(25-24)

x = 2.5 + or - .5

x = 3 or 2

or complete the square

x^2 -5x + 25/4 = -6 +25/4

(x-5/2)^2 = 1/4

x-5/2 = + or -sqr(1/4)

x =5/2 + or - 1/2

x =6/2 or 4/2

x = 3 or 2