Solve x2 + 8x -12 = 0 by completing the square

x2 + 8x =12 x2 + 8x + 16 =12 + 16

(x + 4)2 =28 x + 4 = + 28

{ -4 +2 x=-4 +2

6.3: Relationship of Roots,

Factoring, Graphing &

Solving Equations

If A*B = 0 thenA= 0 or B = 0

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

Solve by factoring:

x2 – x - 6= 0

{-2, 3}

x2 – x - 6= 0

Factors: Solutions:Roots:Graph:

(x+2) (x-3){ -2,3}-2 and 3

x-int at -2 and 3

Equation:

Factors: Solutions:Roots:Graph:

p and q {p, q} (x-p)(x-q)

x-int at p and q

Equation:MULT. and make it = 0

Solve by

Factoring: 2x2 +7x = 152x2 +7x – 15 = 0

(2x-3) (x+5) = 0(2x-3)=0 or (x+5)= 02x=3 or x=-5 x=3/2 or x=-5

Solve by

Factoring: 5x2 – 60=5x5x2 - 5x – 60 = 05(x2 - x – 12) = 0

5(x-4) (x+3)= 0

5=0 x-4=0 or x+3= 0 x=4 or x=-3

Factors: Solutions:Roots:Graph:

{0, –5 }

Equation:

0 and -5

x(x+5)x2 + 5x = 0

x-int at 0 and -5

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

8x2 + 2x – 3 = 0

x2 + 1x/4 – 3/8 = 0

8 8 8

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

13 & 15 or -15 &-13

Factor by

graphing: 2x2 +7x - 15

2x2 +7x – 15 =yRoots: 3/2 and -5

Factors: (x – 3/2) (x+5)(2x – 3) (x + 5)

Check: 2x2 +7x - 15

Factor by

graphing: 4x2 - 100

4x2 - 100 =yRoots: 5 and -5

Factors: (x – 5) (x+5)

4(x – 5) (x + 5)

Check: x2 – 25 NO!