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z2+2z-15=0

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1 Answer

Hi Irish;
z2+2z-15=0
For the FOIL...
FIRST must be (z)(z)=z2
OUTER and INNER must add-up to 2z.
LAST must be (15)(1) or (1)(15) or (5)(3) or (3)(5) and one number must be negative to render the product of -15 and sum of +2.
(z+5)(z-3)=0
Let's FOIL...
FIRST...(z)(z)=x2
OUTER...(z)(-3)=-3z
INNER...(5)(z)=5z
LAST...(5)(-3)=-15
z2-3z+5z-15=0
z2+2z-15=0
(z+5)(z-3)=0
Either or both parenthetical equation(s) must equal zero...
z+5=0...........z-3=0
z=-5.............z=3
 
Let's check our results...
z2+2z-15=0.....................z2+2z-15=0
z=-5...............................z=3
(-5)2+[(2)(-5)]-15............(3)2+[(2)(3)]-15=0
25-10-15=0......................9+6-15=0
0=0.................................0=0