1,148 prompts matching "Solving a surd equation that leads to a quadratic"
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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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Learn: Finding alpha squared plus beta squared from the sum and product
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Worked Example: Finding one over alpha plus one over beta
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Quiz: Finding alpha cubed plus beta cubed
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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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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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Common Mistakes: Adding, subtracting and multiplying two polynomials
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Final Revision: The zeros of a polynomial and where its graph cuts the x-axis
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Learn: The sum of the roots of a cubic read from its coefficients
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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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Quiz: The product of the roots of a cubic
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Practice: Finding the third root of a cubic when two are known
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Spot My Mistake: The relations between roots and coefficients for a quartic
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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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Spot My Mistake: Showing the solution of an inequality on a number line
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