Solving Quadratics with the Formula

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21-Oct-09
Solving Quadratics with the Formula
x -bv(b²- 4ac) 2a
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Solve by factorising x2 2x 15 0 (x 5)(x -
3) 0 x 5 0 ? x -5 x - 3 0 ? x 3 x
-5 and 3
1 x -15 -15 3 x -5 -15 5 x -3 -15 15 x -1
-15 5 3 2
3
1 x -12 -12 2 x -6 -12 3 x -4 -12 4 x -3
-12 6 x 2 -12 12 x 1 -12
Solve by factorising x2 2x 12 0
Will not factorise into integer (whole) numbers
but there is a formula that gives the answer.
4
Solve by formula x2 2x 15 0 x -bv(b²-
4ac) 2a x -2v(2²- 4 x 1 x -
15) 2 x 1 x -2v(4 - -60)
2 x -2v(64) 2
Remember, answers x -5 and x 3
a 1 b 2 c -15
- v64
v64
x -2 8 2 x 6 2 x 3
x -2 - 8 2 x -10 2 x -5
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Solve by formula x2 2x 12 0 x -bv(b²-
4ac) 2a x -2v(2²- 4 x 1 x -
12) 2 x 1 x -2v(4 - -48)
2 x -2v(52) 2
The answers are x -4.6 and x 2.6
a 1 b 2 c -12
- v52
v52
x -2 7.21 2 x 5.21 2 x 2.6
x -2 7.21 2 x -9.21 2 x -4.6
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x -bv(b²- 4ac) 2a
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