1,330 prompts matching "Structured question: new equation with roots 1/alpha and 1/beta"
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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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Worked Example: Finding one over alpha plus one over beta
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Explain Back: Finding alpha squared beta plus alpha beta squared
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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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Worked Example: The difference between a permutation and a combination
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Explain Back: Choosing a committee with a stated number from each of two groups
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Show All Working: Counting the handshakes, or the lines joining n points
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Worked Example: The identities for one plus tan squared and one plus cot squared
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Show All Working: The half angle formulae and the t-substitution
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Worked Example: Solving cos x equals a negative value, and finding both solutions
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Worked Example: The shape, period and range of the cosine curve
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Explain Back: The equation of the line through two given points
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Show All Working: The intersection of a circle and a straight line
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Practice: The ellipse in standard form, and its two axes
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Show All Working: The effect on the standard deviation of adding a constant to every value
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Worked Example: The sign convention for clockwise and anticlockwise moments
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Show All Working: A lift, and the person standing in it
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