1. Solve x2 + 8x -12 = 0
by completing the square
x2 + 8x =12
x2 + 8x + 16 =
(x + 4)2 =28
x + 4 = +Ö 28
x=-4 +2Ö7 }
{ -4 +2Ö7 }

2. 6.3: Relationship of Roots, Factoring, Graphing & Solving Equations

3. If A*B = 0 then
A= 0 or B = 0

4. (x+2) (x-3) = 0 (x+2)=0 or (x-3) = 0 x= -2 or x=3 x2 – x - 6= 0
Solve by factoring:
x2 – x - 6= 0
(x+2) (x-3) = 0
(x+2)=0 or (x-3) = 0
x= -2 or x=3
{-2, 3}

5. Equation: Factors: (x+2) (x-3) Solutions: Roots: { -2,3} Graph:
-2 and 3
x-int at -2 and 3

6. Equation: Factors: (x-p)(x-q) Solutions: Roots: {p, q} Graph: p and q
MULT. and
make it = 0
Equation:
Factors:
Solutions:
Roots:
Graph:
(x-p)(x-q)
{p, q}
p and q
x-int at p and q

7. 2x2 +7x = 15 2x2 +7x – 15 = 0 (2x-3) (x+5) = 0 (2x-3)=0 or (x+5)= 0
Solve by
Factoring:
2x2 +7x – 15 = 0
(2x-3) (x+5) = 0
(2x-3)=0 or (x+5)= 0
2x=3 or x=-5
x=3/2 or x=-5

8. 5x2 – 60=5x 5x2 - 5x – 60 = 0 5(x2 - x – 12) = 0 5(x-4) (x+3)= 0
Solve by
Factoring:
5x2 - 5x – 60 = 0
5(x2 - x – 12) = 0
5(x-4) (x+3)= 0
5=0 x-4=0 or x+3= 0
x=4 or x=-3

9. Equation: x2 + 5x = 0 Factors: x(x+5) Solutions: Roots: {0, –5 }
Graph:
x(x+5)
{0, –5 }
0 and -5
x-int at 0 and -5

10. Write two equations that has roots of ½ and –3/4
(x – ½) (x + 3/4 ) =0
x2 + 3x/4 – x/2 – 3/8 = 0
x2 + 1x/4 – 3/8 = 0
8x2 + 2x – 3 = 0

11. Find two consecutive odd
integers whose product is 195
x (x+2) = 195
x2 + 2x = 195
x2 + 2x – 195 = 0
(x-13)(x+15) =0
x-13 = 0 or x+15 =0
x=13 x=-15
13 & 15 or -15 &-13

12. 2x2 +7x - 15 2x2 +7x – 15 =y Roots: 3/2 and -5 (2x – 3) (x + 5)
Factor by
graphing:
2x2 +7x – 15 =y
Roots: 3/2 and -5
Factors: (x – 3/2) (x+5)
(2x – 3) (x + 5)
Check: 2x2 +7x - 15

13. 4x2 - 100 4x2 - 100 =y Roots: 5 and -5 4(x – 5) (x + 5) Factor by
graphing:
4x =y
Roots: 5 and -5
Factors: (x – 5) (x+5)
Check: x2 – NO!
4(x – 5) (x + 5)