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| Methods of completing a square and to derive the formula for the solution of the quadratic equation |
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| Divide by 'a' throughout. |
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| Multiplying by 4 times the coefficient of x2 on both sides i.e., 4a. |
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| 4a2x2 + 4abx = -4ac [Transposing 4ac to RHS] |
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| (2ax)2 + 2(2ax)b = -4ac [Writing 4a2x2 = (2ax)2, |
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| 4abx = 2(2ax)b] |
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| (2ax)2 + 2(2ax)b +b2= b2 - 4ac |
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| [Adding b2 to both sides (square of the coefficient of x)] |
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| (2ax + b)2 = b2 - 4ac [a2 + 2ab + b2 = (a+b)2] |
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| Note: |
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| i) Upto step 6 in the I Method and upto Step 7 in the II Method, gives the process of completing the square. |
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| ii) The quadratic equation has two roots. |
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| (i.e., there are two values for x) |
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| is b2 - 4ac. This is usually denoted by D or D. D determines the nature of the roots. |
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