1,334 prompts matching "Solving an equation with a fractional exponent on x"
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Worked Example: The intersection of two overlapping sets
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Common Mistakes: Showing that intersection distributes over union
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Worked Example: Testing whether a binary operation is closed on a given set
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Practice: Testing a binary operation for associativity
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Common Mistakes: A binary operation defined by arithmetic modulo n
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Practice: Rationalising a denominator of the form root a
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Explain Back: The laws of logarithms for a product and for a quotient
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Worked Example: The discriminant, and what each of its three cases means
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Explain Back: The range of values of k for which the roots are real
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Worked Example: Finding one over alpha plus one over beta
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Practice: Finding alpha minus beta from the sum and the product
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Show All Working: Finding a coefficient given a stated relation between the roots
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Common Mistakes: Symmetric functions when the three roots of a cubic are involved
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Worked Example: Evaluating a polynomial by substitution
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Practice: Factorising a cubic completely once one factor is known
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Explain Back: Finding an unknown coefficient given that a stated factor divides the polynomial
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Show All Working: Three roots in arithmetic progression in a cubic
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Common Mistakes: Three roots in geometric progression in a cubic
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Worked Example: The number of arrangements of n different objects in a row
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