1,235 prompts matching "Structured question: quadratic formula with exact surd answer"
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Explain Back: The laws of logarithms for a product and for a quotient
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Common Mistakes: Solving an exponential equation using logarithms
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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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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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Explain Back: Finding alpha squared beta plus alpha beta squared
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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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Common Mistakes: Adding, subtracting and multiplying two polynomials
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Worked Example: The sum of the products of the roots of a cubic taken two at a time
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Practice: Finding the third root of a cubic when two are known
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Explain Back: Forming a cubic equation whose three roots are given
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Common Mistakes: Three roots in geometric progression in a cubic
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Explain Back: Solving an inequality that involves a modulus
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Common Mistakes: The range of values of x for which an expression stays positive
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Worked Example: The number of arrangements of n different objects in a row
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Practice: Arrangements when some of the objects are identical
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