Quadratic Equation Formula
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Method
mentioned in most textbook |
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The given quadratic equation
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Move c to the right hand side
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Divide by a
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Add a term to both sides for
completing square
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Complete square,
Join the terms on right hand side
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Take square root
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Solve for x
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Sridhara’s
Method (circa 1025 A.D.) |
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The given quadratic equation
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Move c to the right hand side
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Multiply by 4a
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Add
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Complete square,
Join the terms on right hand side
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Take square root
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Solve for x
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Vieta’sMethod
(circa 1540 A.D.) |
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The given quadratic equation
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Substitute
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Expand
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Simplify
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Move terms
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Take square root
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Change y to x
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Solve for x
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Why we use the substitution :
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The given quadratic equation
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Substitute x = y + d
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Expand and group terms
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We don’t
need the y-term, we therefore put the coefficient of y zero |
2ad + b = 0
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Harriot’s
Method (circa 1630 A.D.) |
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The given quadratic equation
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Divide by a
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Let a, b are roots, then the quadratic equation is the
same as :
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Comparing coefficients of quadratic
equations (1) & (2)
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Consider the identity
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Find a - b
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We have two equations in
a + b, a - b
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Solve for a , b
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