Help with this math question

Question

The roots of the equation x^2+bx+c=0 are −4 and 2. Find b.

Answer 1

x² + bx + c = 0 is a polynomial equation.  It has two roots    [given:  (-4) and 2]

 

      We can write the equation this way   [because of The Multiplicative Property of Zero:  If a*b=0 then either a=0 or b=0 or both]:

 

        (x-(-4))(x-2) = 0

 

         (x+4)(x-2) = 0

         x² - 2x + 4x - 8 = 0             [use F-O-I-L]

         x² +2x - 8 = 0                     [combine like terms]

         x² +bx + c = 0

 

     So, 

       b = 2

       c = (-8)                     [because coefficients of like terms must be equal; note: set a=1 by dividing, if needed]

Answer 2

(x + 4)(x - 2) = x² + 2x - 8 = ax² + bx + c

 

Compare and see that

 

a = 1

b = 2

c = -8