Practice Solving Quadratic Equations |
INSTRUCTIONS:
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QUESTIONS
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1) Write the solutions by inspection.
a) ( x 7 ) ( x + 3 ) = 0
b) (2x 4 ) ( x + 6 ) = 0
c) ( 5x 3 ) ( 2x + 7 ) = 0
d) ( 4x 2 ) ( 9x + 3 ) = 0
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2) Solve these quadratic equations by factoring.
a) x² + 2x 15 = 0
b) 5x² + 10x = 0
c) 2x² + 3x 5 = 0
d) 10x² x 3 = 0
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3) Solve by completing the square. State the number and nature of the solutions.
a) x² 6x = 3
b) y² 2y = 2
c) 2 x² = 3 x
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4) Use the quadratic formula to solve these. State the number and nature of the solutions.
a) x² + 5x = 3
b) 9 x² 6x + 1 = 0
c) 3 x² 2x = 1
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SOLUTIONS
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1) Write the solutions by inspection.
a) ( x 7 ) ( x + 3 ) = 0 | x = 7 | or | x = 3 |
b) ( 2x 4 ) ( x + 6 ) = 0 | x = 2 | or | x = 6 |
c) ( 5x 3 ) ( 2x + 7 ) = 0 | x = 3/5 | or | x = 7/2 |
d) ( 4x 2 ) ( 9x + 3 ) = 0 | x = ½ | or | x = 1/3 |
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2) Solve these quadratic equations by factoring.
x² + 2x 15 = 0 | ( x + 5 ) ( x 3 ) = 0 | x = 5 | x = 3 |
5x² + 10x = 0 | 5x ( x + 2 ) = 0 | x = 2 | x = 0 |
2x² + 3x 5 = 0 | (2x + 5 ) ( x 1 ) = 0 | x = 5/2 | x = 1 |
10x² x 3 = 0 | ( 2x + 1 ) ( 5x 3 ) = 0 | x = ½ | x = 3/5 |
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3) Solve by completing the square. State the number and nature of the solutions.
a) x² 6x + 3 = 0 becomes x² 6x + 9 9 + 3 = 0 becomes ( x 3 )² 6 = 0
( x 3 )² = 6 becomes
There are 2 Real solutions.
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b) y² 2y 2 = 0 becomes y² 2y + 1 1 2 = 0 becomes ( y 1) ² 3 = 0
( y 1 )² = 3 becomes
There are 2 Real solutions.
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c) 2 x² + x 3 = 0 becomes 2( x² + ½ x ) 3 = 0 becomes 2( x² + ½ x + 1/16 ) 3 = 0
2( x + ¼ )² + 1/8 24/8 = 0 becomes
There are 2 Real solutions.
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4) Use the quadratic formula to solve these. State the number and nature of the solutions.
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a) x² + 5x 3 = 0 a = 1, b = 5, c = 3 becomes
There are 2 Real roots or solutions.
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b) 9 x² 6x + 1 = 0 a = 9, b = 6, c = 1 becomes
There is 1 Real root or solution. (also called 2 equal roots??)
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c) 3x² 2x + 1 = 0 a = 3, b = 2, c = 1 becomes
There are no Real roots. There are 2 complex or imaginary roots
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